On some geometric properties of sequence spaces of generalized arithmetic divisor sum function
Recently, some new sequence spaces ℓ p ( A α ) ( 0 < p < ∞ ) , c 0 ( A α ) , c ( A α ) , and ℓ ∞ ( A α ) have been studied by Yaying et al. (Forum Math., 2024 , https://doi.org/10.1515/forum-2023-0138 ) as matrix domains of A α = ( a n , v α ) , where a m , v α = { v α ρ ( α ) ( m ) , v ∣ m ,...
Saved in:
| Published in | Journal of inequalities and applications Vol. 2024; no. 1; pp. 128 - 10 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
27.09.2024
Springer Nature B.V SpringerOpen |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1029-242X 1025-5834 1029-242X |
| DOI | 10.1186/s13660-024-03208-z |
Cover
Loading…
| Abstract | Recently, some new sequence spaces
ℓ
p
(
A
α
)
(
0
<
p
<
∞
)
,
c
0
(
A
α
)
,
c
(
A
α
)
, and
ℓ
∞
(
A
α
)
have been studied by Yaying et al. (Forum Math.,
2024
,
https://doi.org/10.1515/forum-2023-0138
) as matrix domains of
A
α
=
(
a
n
,
v
α
)
, where
a
m
,
v
α
=
{
v
α
ρ
(
α
)
(
m
)
,
v
∣
m
,
0
,
v
∤
m
,
and
ρ
(
α
)
(
m
)
:
=
sum of the
α
th
power of the positive divisors of
m
∈
N
. They obtained their duals, matrix transformations and associated compact matrix operators for these matrix classes.
This article deals with some geometric properties of these sequence spaces. |
|---|---|
| AbstractList | Recently, some new sequence spaces ℓp(Aα)(0<p<∞), c0(Aα), c(Aα), and ℓ∞(Aα) have been studied by Yaying et al. (Forum Math., 2024, https://doi.org/10.1515/forum-2023-0138) as matrix domains of Aα=(an,vα), where am,vα={vαρ(α)(m),v∣m,0,v∤m,and ρ(α)(m):= sum of the αth power of the positive divisors of m∈N. They obtained their duals, matrix transformations and associated compact matrix operators for these matrix classes.This article deals with some geometric properties of these sequence spaces. Abstract Recently, some new sequence spaces ℓ p ( A α ) $\ell _{p}(\mathfrak{A}^{\alpha })$ ( 0 < p < ∞ ) $(0< p<\infty )$ , c 0 ( A α ) $c_{0}(\mathfrak{A}^{\alpha })$ , c ( A α ) $c(\mathfrak{A}^{\alpha })$ , and ℓ ∞ ( A α ) $\ell _{\infty }(\mathfrak{A}^{\alpha })$ have been studied by Yaying et al. (Forum Math., 2024, https://doi.org/10.1515/forum-2023-0138 ) as matrix domains of A α = ( a n , v α ) $\mathfrak{A}^{\alpha }=(a_{n,v}^{\alpha })$ , where a m , v α = { v α ρ ( α ) ( m ) , v ∣ m , 0 , v ∤ m , $$ a_{\mathfrak{m},v}^{\alpha }=\left \{ \textstyle\begin{array}{c@{\quad}c@{\quad}c} \dfrac{v^{\alpha }}{\rho ^{(\alpha )}(\mathfrak{m})} & , & v\mid \mathfrak{m}, \\ 0 & , & v\nmid \mathfrak{m},\end{array}\displaystyle \right . $$ and ρ ( α ) ( m ) : = $\rho ^{(\alpha )}(\mathfrak{m}):=$ sum of the α th $\alpha ^{\text{th}}$ power of the positive divisors of m ∈ N $\mathfrak{m}\in \mathbb{N}$ . They obtained their duals, matrix transformations and associated compact matrix operators for these matrix classes. This article deals with some geometric properties of these sequence spaces. Recently, some new sequence spaces ℓ p ( A α ) ( 0 < p < ∞ ) , c 0 ( A α ) , c ( A α ) , and ℓ ∞ ( A α ) have been studied by Yaying et al. (Forum Math., 2024 , https://doi.org/10.1515/forum-2023-0138 ) as matrix domains of A α = ( a n , v α ) , where a m , v α = { v α ρ ( α ) ( m ) , v ∣ m , 0 , v ∤ m , and ρ ( α ) ( m ) : = sum of the α th power of the positive divisors of m ∈ N . They obtained their duals, matrix transformations and associated compact matrix operators for these matrix classes. This article deals with some geometric properties of these sequence spaces. |
| ArticleNumber | 128 |
| Author | Mursaleen, Mohammad Herawati, Elvina |
| Author_xml | – sequence: 1 givenname: Mohammad surname: Mursaleen fullname: Mursaleen, Mohammad email: mursaleenm@gmail.com organization: China Medical University Hospital, China Medical University (Taiwan), Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara, Department of Mathematics, Aligarh Muslim University – sequence: 2 givenname: Elvina surname: Herawati fullname: Herawati, Elvina organization: Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara |
| BookMark | eNp9kUlLBDEQhYMouP4BTwHPrZWl0-mjiBsIXhQ8GdLp6jHDTDImPYLz6422qCcvWYr3vqTq7ZPtEAMScszglDGtzjITSkEFXFYgOOhqs0X2GPC24pI_bf8575L9nOcAnAkt98jzfaA5LpHOsKxj8o6uUlxhGj1mGgea8XWNwSHNK-um0gwDJrvwG-ypTX58Kcbi6_2bzzHRvF7SYR3c6GM4JDuDXWQ8-t4PyOPV5cPFTXV3f317cX5XOaFhrKyCjjXKgkPsVMtwaDsloWm1tCCtc43i5Q6yUeg6xZqaKV33fYsSHddaHJDbidtHOzer5Jc2vZtovfkqxDQztrTkFmhayWvGur6GDiRz3FrHheqgcKTuhCysk4lVBlF6z6OZx3UK5ftGMAa1bMowi4pPKpdizgmHn1cZmM9MzJSJKZmYr0zMppjEZMpFHGaYftH_uD4AffmRjA |
| Cites_doi | 10.1216/rmj.2022.52.1867 10.1002/mma.6501 10.7153/oam-2019-13-40 10.1142/S1793557122501406 10.1155/2014/427382 10.1515/forum-2023-0138 10.1201/9781003015116 10.1002/mma.6537 10.1006/jmaa.1997.5657 10.56405/dngcrj.2020.05.01.07 10.1186/s13660-024-03149-7 10.1007/978-1-4757-5579-4 10.1007/BF01194848 10.1007/s40009-016-0525-2 10.1007/978-1-4612-0603-3 10.1090/S0002-9947-1940-0004094-3 10.1007/s00009-019-1442-7 10.1016/j.na.2005.09.038 10.1007/s40009-020-00910-6 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2024 The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s) 2024 – notice: The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | C6C AAYXX CITATION 7TB 8FD 8FE 8FG ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ HCIFZ JQ2 K7- KR7 L6V M7S P5Z P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PTHSS DOA |
| DOI | 10.1186/s13660-024-03208-z |
| DatabaseName | Springer Nature OA Free Journals (ODIN) CrossRef Mechanical & Transportation Engineering Abstracts Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One Community College ProQuest Central Korea Engineering Research Database ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database Civil Engineering Abstracts ProQuest Engineering Collection Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition Engineering Collection DOAJ Directory of Open Access Journals (WRLC) |
| DatabaseTitle | CrossRef Publicly Available Content Database Computer Science Database ProQuest Central Student Technology Collection Technology Research Database ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts Engineering Database ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: C6C name: SpringerOpen Free (Free internet resource, activated by CARLI) url: http://www.springeropen.com/ sourceTypes: Publisher – sequence: 2 dbid: DOA name: DOAJ Directory of Open Access Journals (ODIN) url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 3 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1029-242X |
| EndPage | 10 |
| ExternalDocumentID | oai_doaj_org_article_942511bd50b041c2aac236b0c2848b34 10_1186_s13660_024_03208_z |
| GroupedDBID | -A0 0R~ 29K 2WC 4.4 40G 5GY 5VS 8FE 8FG 8R4 8R5 AAFWJ AAJSJ AAKKN ABDBF ABEEZ ABFTD ABJCF ACACY ACGFO ACGFS ACIPV ACIWK ACUHS ACULB ADBBV ADINQ AENEX AFGXO AFKRA AFPKN AHBYD AHYZX AIAGR ALMA_UNASSIGNED_HOLDINGS AMKLP AMTXH ARAPS BCNDV BENPR BGLVJ C24 C6C CCPQU CS3 D-I DU5 EBLON EBS ESX GROUPED_DOAJ HCIFZ J9A K6V K7- KQ8 L6V M7S M~E OK1 P2P P62 PIMPY PROAC PTHSS Q2X REM RHU RNS RSV SMT SOJ TUS U2A ~8M AASML AAYXX AMVHM CITATION OVT PHGZM PHGZT 7TB 8FD ABUWG AZQEC DWQXO FR3 GNUQQ JQ2 KR7 PKEHL PQEST PQGLB PQQKQ PQUKI PUEGO |
| ID | FETCH-LOGICAL-c380t-a60b176a0ceeb691ef9b6407984a04acc7626400476ecb61751685dd9e4ec2883 |
| IEDL.DBID | U2A |
| ISSN | 1029-242X 1025-5834 |
| IngestDate | Wed Aug 27 01:30:46 EDT 2025 Fri Jul 25 12:20:44 EDT 2025 Tue Jul 01 04:06:24 EDT 2025 Fri Feb 21 02:41:47 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | 47B07 Sequence spaces Geometric properties 47B37 46A45 46B45 Arithmetic divisor sum function 40C05 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c380t-a60b176a0ceeb691ef9b6407984a04acc7626400476ecb61751685dd9e4ec2883 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://link.springer.com/10.1186/s13660-024-03208-z |
| PQID | 3110547102 |
| PQPubID | 237789 |
| PageCount | 10 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_942511bd50b041c2aac236b0c2848b34 proquest_journals_3110547102 crossref_primary_10_1186_s13660_024_03208_z springer_journals_10_1186_s13660_024_03208_z |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2024-09-27 |
| PublicationDateYYYYMMDD | 2024-09-27 |
| PublicationDate_xml | – month: 09 year: 2024 text: 2024-09-27 day: 27 |
| PublicationDecade | 2020 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: Heidelberg |
| PublicationTitle | Journal of inequalities and applications |
| PublicationTitleAbbrev | J Inequal Appl |
| PublicationYear | 2024 |
| Publisher | Springer International Publishing Springer Nature B.V SpringerOpen |
| Publisher_xml | – name: Springer International Publishing – name: Springer Nature B.V – name: SpringerOpen |
| References | García-FalsetJ.The fixed point property in Banach spaces with the NUS-propertyJ. Math. Anal. Appl.19972152532542149076710.1006/jmaa.1997.5657 NivenI.ZuckermanH.S.MontgomeryH.L.An Introduction to the Theory of Numbers1991New YorkWiley YayingT.SaikiaN.On sequence spaces defined by arithmetic function and Hausdorff measure of non-compactnessRocky Mt. J. Math.20225251867188510.1216/rmj.2022.52.1867 YayingT.Arithmetic continuity in cone metric spaceDera Natung Gov. Coll. Res. J.202051556210.56405/dngcrj.2020.05.01.07 GurariiV.I.Differential properties of the convexity moduli of Banach spacesMat. Issled.19672141148211245(Russian) HudzikH.KarakayaV.MursaleenM.SimsekN.Banach-Saks type and Gurariı̌ modulus of convexity of some Banach sequence spacesAbstr. Appl. Anal.2014201410.1155/2014/427382 MursaleenM.BaşarF.Sequence Spaces: Topics in Modern Summability Theory2020Boca RatonCRC Press10.1201/9781003015116 İlkhanM.KaraE.E.UstaF.Compact operators on the Jordan totient sequence spacesMath. Methods Appl. Sci.20214476667675425847810.1002/mma.6537 KnaustH.Orlicz sequence spaces of Banach-Saks typeArch. Math. (Basel)1992596562565118987410.1007/BF01194848 İlkhanM.ŞimşekN.KaraE.E.A new regular infinite matrix defined by Jordan totient function and its matrix domain in ℓp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ell _{p}$\end{document}Math. Methods Appl. Sci.20214476227633425847410.1002/mma.6501 İlkhanM.Matrix domain of a regular matrix derived by Euler totient function in the spaces c0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$c_{0}$\end{document} and cMediterr. J. Math.202017411758910.1007/s00009-019-1442-7 PhillipsR.S.On linear transformationsTrans. Am. Math. Soc.19404851654110.1090/S0002-9947-1940-0004094-3 ApostolT.M.Introduction to Analytic Number Theory1976New YorkSpringer10.1007/978-1-4757-5579-4 García-FalsetJ.Stability and fixed points for nonexpansive mappingsHoust. J. Math.19942034955061287990 BrahaN.YayingT.MursaleenM.Sequence spaces derived by qλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$q^{\lambda}$\end{document} operators in ℓp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ell _{p}$\end{document} spaces and their geometric propertiesJ. Inequal. Appl.20242024475239510.1186/s13660-024-03149-7 YayingT.HazarikaB.Lacunary arithmetic statistical convergenceNat. Acad. Sci. Lett.202043547551416357110.1007/s40009-020-00910-6 Ayman MursaleenM.A note on matrix domains of Copson matrix of order α and compact operatorsAsian-Eur. J. Math.2022157444902710.1142/S1793557122501406 İlkhanM.KaraE.E.A new Banach space defined by Euler totient matrix operatorOper. Matrices2019132527544398046010.7153/oam-2019-13-40 YayingT.SaikiaN.MursaleenM.New sequence spaces derived by using generalized arithmetic divisor sum function and compact operatorsForum Math.202410.1515/forum-2023-0138 YayingT.HazarikaB.On arithmetical summability and multiplier sequencesNat. Acad. Sci. Lett.2017404346360526510.1007/s40009-016-0525-2 MegginsonR.E.An Introduction to Banach Space Theory1998New YorkSpringer10.1007/978-1-4612-0603-3 MursaleenM.BaşarF.AltayB.On the Euler sequence spaces which include the spaces lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$l_{p}$\end{document} and l∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$l_{\infty }$\end{document}Nonlinear Anal.2006653707717223108410.1016/j.na.2005.09.038 M. İlkhan (3208_CR8) 2020; 17 T. Yaying (3208_CR19) 2017; 40 J. García-Falset (3208_CR4) 1994; 20 M. İlkhan (3208_CR10) 2021; 44 I. Niven (3208_CR16) 1991 M. İlkhan (3208_CR11) 2021; 44 R.E. Megginson (3208_CR13) 1998 N. Braha (3208_CR3) 2024; 2024 V.I. Gurarii (3208_CR6) 1967; 2 M. Ayman Mursaleen (3208_CR2) 2022; 15 H. Hudzik (3208_CR7) 2014; 2014 M. İlkhan (3208_CR9) 2019; 13 T. Yaying (3208_CR22) 2024 J. García-Falset (3208_CR5) 1997; 215 R.S. Phillips (3208_CR17) 1940; 48 T. Yaying (3208_CR20) 2020; 43 M. Mursaleen (3208_CR15) 2006; 65 T. Yaying (3208_CR21) 2022; 52 T.M. Apostol (3208_CR1) 1976 H. Knaust (3208_CR12) 1992; 59 T. Yaying (3208_CR18) 2020; 5 M. Mursaleen (3208_CR14) 2020 |
| References_xml | – reference: YayingT.SaikiaN.MursaleenM.New sequence spaces derived by using generalized arithmetic divisor sum function and compact operatorsForum Math.202410.1515/forum-2023-0138 – reference: ApostolT.M.Introduction to Analytic Number Theory1976New YorkSpringer10.1007/978-1-4757-5579-4 – reference: NivenI.ZuckermanH.S.MontgomeryH.L.An Introduction to the Theory of Numbers1991New YorkWiley – reference: YayingT.Arithmetic continuity in cone metric spaceDera Natung Gov. Coll. Res. J.202051556210.56405/dngcrj.2020.05.01.07 – reference: YayingT.HazarikaB.Lacunary arithmetic statistical convergenceNat. Acad. Sci. Lett.202043547551416357110.1007/s40009-020-00910-6 – reference: İlkhanM.KaraE.E.UstaF.Compact operators on the Jordan totient sequence spacesMath. Methods Appl. Sci.20214476667675425847810.1002/mma.6537 – reference: MursaleenM.BaşarF.AltayB.On the Euler sequence spaces which include the spaces lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$l_{p}$\end{document} and l∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$l_{\infty }$\end{document}Nonlinear Anal.2006653707717223108410.1016/j.na.2005.09.038 – reference: PhillipsR.S.On linear transformationsTrans. Am. Math. Soc.19404851654110.1090/S0002-9947-1940-0004094-3 – reference: KnaustH.Orlicz sequence spaces of Banach-Saks typeArch. Math. (Basel)1992596562565118987410.1007/BF01194848 – reference: İlkhanM.Matrix domain of a regular matrix derived by Euler totient function in the spaces c0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$c_{0}$\end{document} and cMediterr. J. Math.202017411758910.1007/s00009-019-1442-7 – reference: GurariiV.I.Differential properties of the convexity moduli of Banach spacesMat. Issled.19672141148211245(Russian) – reference: YayingT.SaikiaN.On sequence spaces defined by arithmetic function and Hausdorff measure of non-compactnessRocky Mt. J. Math.20225251867188510.1216/rmj.2022.52.1867 – reference: YayingT.HazarikaB.On arithmetical summability and multiplier sequencesNat. Acad. Sci. Lett.2017404346360526510.1007/s40009-016-0525-2 – reference: García-FalsetJ.Stability and fixed points for nonexpansive mappingsHoust. J. Math.19942034955061287990 – reference: İlkhanM.KaraE.E.A new Banach space defined by Euler totient matrix operatorOper. Matrices2019132527544398046010.7153/oam-2019-13-40 – reference: Ayman MursaleenM.A note on matrix domains of Copson matrix of order α and compact operatorsAsian-Eur. J. Math.2022157444902710.1142/S1793557122501406 – reference: BrahaN.YayingT.MursaleenM.Sequence spaces derived by qλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$q^{\lambda}$\end{document} operators in ℓp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ell _{p}$\end{document} spaces and their geometric propertiesJ. Inequal. Appl.20242024475239510.1186/s13660-024-03149-7 – reference: HudzikH.KarakayaV.MursaleenM.SimsekN.Banach-Saks type and Gurariı̌ modulus of convexity of some Banach sequence spacesAbstr. Appl. Anal.2014201410.1155/2014/427382 – reference: İlkhanM.ŞimşekN.KaraE.E.A new regular infinite matrix defined by Jordan totient function and its matrix domain in ℓp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ell _{p}$\end{document}Math. Methods Appl. Sci.20214476227633425847410.1002/mma.6501 – reference: MegginsonR.E.An Introduction to Banach Space Theory1998New YorkSpringer10.1007/978-1-4612-0603-3 – reference: García-FalsetJ.The fixed point property in Banach spaces with the NUS-propertyJ. Math. Anal. Appl.19972152532542149076710.1006/jmaa.1997.5657 – reference: MursaleenM.BaşarF.Sequence Spaces: Topics in Modern Summability Theory2020Boca RatonCRC Press10.1201/9781003015116 – volume: 52 start-page: 1867 issue: 5 year: 2022 ident: 3208_CR21 publication-title: Rocky Mt. J. Math. doi: 10.1216/rmj.2022.52.1867 – volume-title: An Introduction to the Theory of Numbers year: 1991 ident: 3208_CR16 – volume: 44 start-page: 7622 year: 2021 ident: 3208_CR11 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.6501 – volume: 13 start-page: 527 issue: 2 year: 2019 ident: 3208_CR9 publication-title: Oper. Matrices doi: 10.7153/oam-2019-13-40 – volume: 15 issue: 7 year: 2022 ident: 3208_CR2 publication-title: Asian-Eur. J. Math. doi: 10.1142/S1793557122501406 – volume: 2 start-page: 141 year: 1967 ident: 3208_CR6 publication-title: Mat. Issled. – volume: 2014 year: 2014 ident: 3208_CR7 publication-title: Abstr. Appl. Anal. doi: 10.1155/2014/427382 – year: 2024 ident: 3208_CR22 publication-title: Forum Math. doi: 10.1515/forum-2023-0138 – volume: 20 start-page: 495 issue: 3 year: 1994 ident: 3208_CR4 publication-title: Houst. J. Math. – volume-title: Sequence Spaces: Topics in Modern Summability Theory year: 2020 ident: 3208_CR14 doi: 10.1201/9781003015116 – volume: 44 start-page: 7666 year: 2021 ident: 3208_CR10 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.6537 – volume: 215 start-page: 532 issue: 2 year: 1997 ident: 3208_CR5 publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1997.5657 – volume: 5 start-page: 55 issue: 1 year: 2020 ident: 3208_CR18 publication-title: Dera Natung Gov. Coll. Res. J. doi: 10.56405/dngcrj.2020.05.01.07 – volume: 2024 year: 2024 ident: 3208_CR3 publication-title: J. Inequal. Appl. doi: 10.1186/s13660-024-03149-7 – volume-title: Introduction to Analytic Number Theory year: 1976 ident: 3208_CR1 doi: 10.1007/978-1-4757-5579-4 – volume: 59 start-page: 562 issue: 6 year: 1992 ident: 3208_CR12 publication-title: Arch. Math. (Basel) doi: 10.1007/BF01194848 – volume: 40 start-page: 43 year: 2017 ident: 3208_CR19 publication-title: Nat. Acad. Sci. Lett. doi: 10.1007/s40009-016-0525-2 – volume-title: An Introduction to Banach Space Theory year: 1998 ident: 3208_CR13 doi: 10.1007/978-1-4612-0603-3 – volume: 48 start-page: 516 year: 1940 ident: 3208_CR17 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1940-0004094-3 – volume: 17 year: 2020 ident: 3208_CR8 publication-title: Mediterr. J. Math. doi: 10.1007/s00009-019-1442-7 – volume: 65 start-page: 707 issue: 3 year: 2006 ident: 3208_CR15 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2005.09.038 – volume: 43 start-page: 547 year: 2020 ident: 3208_CR20 publication-title: Nat. Acad. Sci. Lett. doi: 10.1007/s40009-020-00910-6 |
| SSID | ssj0021384 ssib044744598 ssib008501289 |
| Score | 2.343884 |
| Snippet | Recently, some new sequence spaces
ℓ
p
(
A
α
)
(
0
<
p
<
∞
)
,
c
0
(
A
α
)
,
c
(
A
α
)
, and
ℓ
∞
(
A
α
)
have been studied by Yaying et al. (Forum Math.,
2024... Recently, some new sequence spaces ℓp(Aα)(0<p<∞), c0(Aα), c(Aα), and ℓ∞(Aα) have been studied by Yaying et al. (Forum Math., 2024,... Abstract Recently, some new sequence spaces ℓ p ( A α ) $\ell _{p}(\mathfrak{A}^{\alpha })$ ( 0 < p < ∞ ) $(0< p<\infty )$ , c 0 ( A α )... |
| SourceID | doaj proquest crossref springer |
| SourceType | Open Website Aggregation Database Index Database Publisher |
| StartPage | 128 |
| SubjectTerms | Analysis Applications of Mathematics Approximation Arithmetic divisor sum function Geometric properties Mathematical functions Mathematics Mathematics and Statistics Operators (mathematics) Prime numbers Sequence spaces |
| SummonAdditionalLinks | – databaseName: DOAJ Directory of Open Access Journals (WRLC) dbid: DOA link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT9wwELYqTr3QB1Tddql84AbW2vEj9rEgVggJuIDEqZbtOLQHErRZLvvrO5MHsJWqXnrJwbEiax6eb2LPN4QcijIIWdaK2SAUUy5kFmIBiatxyRhVGyGwwPnyypzfqos7ffeq1RfeCRvogQfBLZxCEBwrzSNXIhUhpEKayBPsqzbKngkUYt6UTI2plpBWTSUy1iw6IY3hDOIRw4bhlm22wlDP1r8FMf84Fe2DzfI92R1RIv0-rO4DeZObj-TdiBjp6I_dHvlx3dCufcj0PsMTyfbpI_5dXyFNKm1rOt2UprBxpGHofiCa_rWBL0GivP75gHWMFOuyunZFwTIpBjtU2D65XZ7dnJ6zsWMCS9LyNQuGR1GawCH0ReNErl3EkzpnVeAqpARbn0GvLU1OEcCLFsbqqnJZ5YR9hz-RnaZt8mdClZS6UiFUiUdI4UqrdZSS18HpOuQQZuRoEqB_HIgxfJ9QWOMHcXsQt-_F7TczcoIyfp6JpNb9AKjaj6r2_1L1jMwnDfnR0zovAb9ohThpRo4nrb28_vuSvvyPJX0lb4veqhwryjnZWa-e8gGglHX81hvkb9eT4gc priority: 102 providerName: Directory of Open Access Journals – databaseName: ProQuest Technology Collection dbid: 8FG link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV07j9QwELbgaGh4I5Y7kAs6sM6Ox45dIUAsJySg4aSrsGzHWShus2yWZn_9eRxnT4cETQonsqJ5fTMezwwhr0TrhWx7YMYLYGB9Yj40OXDVNmoNvRYCC5y_fNVn5_D5Ql3UA7exXqucbWIx1N0Q8Yz8VGacUoB4-Hbzm-HUKMyu1hEat8kdkZEGJdwsPx3kySg0vwe4BmgBlD1kGRohy0RigSNdlZEwF9UYfToKqTVnGcEYjhg3bH8DuEp__xtO6V951AJPywfkXvUr6btJEB6SW2n9iNyvPiatGjw-Jj--rek4XCa6SvmJ7fnpBs_jt9hYlQ49ne9W02xq4rS0mlpT_9rnnXJovft5iZWPFCu5xmFLM3EowiOy-Ak5X378_uGM1RkLLErDd8xrHkSrPc9gGbQVqbcBc3vWgOfgY8zGUqOetzrFkN0dJbRRXWcTpIiTip-So_WwTs8IBSlVB953kYcc9LVGqSAl771VvU_eL8jrmYBuM7XScCUEMdpN5HaZ3K6Q2-0X5D3S-PAltsEuC8N25apWOQsYIYVO8cxdERvvYyN14PnPwAQJC3Iyc8hV3RzdtSQtyJuZa9ev__1Lz_-_2zG52xR5saxpT8jRbvsnvcgeyy68LGJ5BYai41c priority: 102 providerName: ProQuest |
| Title | On some geometric properties of sequence spaces of generalized arithmetic divisor sum function |
| URI | https://link.springer.com/article/10.1186/s13660-024-03208-z https://www.proquest.com/docview/3110547102 https://doaj.org/article/942511bd50b041c2aac236b0c2848b34 |
| Volume | 2024 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3Nb9MwFLfYdoHDgAFa2Vb5wA0s7Pgj9rGrVqZKGwiotBOW7TiFw5qpKZf-9Xt2kqKhceDyIjlOZL0Pv_ez_Z4ResdKx3hZC6IdE0QYF4nzBQBXZYJSolaMpQTnq2t1uRDzG3nTJ4W1w2n3YUsyz9TZrLX62DKuFCXgU0i69FuT7R46kIDdk14viskOZjGuxZAe8-h3D1xQrtT_ILz8a0c0O5rZC3TYR4h40on0JXoSV0foeR8t4t4W2yP07GpXcbV9hX58XuG2uY14GYGmsvv4Lq2zr1PBVNzUeDgzjWEKCV3Tsis5_WsL_wXIvPl5mzIaccrQaps1Bh3Fye0l0b1Gi9nF9-kl6e9OIIFruiFOUc9K5Sg4Qa8Mi7Xxac_OaOGocCHAJKiS_ZYqBg9hjGRKy6oyUcSQbiB-g_ZXzSoeIyw4l5VwrgrUA5grtZSec1o7I2sXnRuh9wM77V1XIsNmaKGV7Zhvgfk2M99uR-g8cXzXM5W3zg3Neml7a7FGJOTjK0k9FSwUzoWCK09hZEJ7LkbodJCX7W2utRwiGSlSxDRCHwYZ_nn97yG9_b_uJ-hpkbXJkKI8Rfub9e94BpHJxo_RnqCfgOoZ0IPJZP5tDs_zi-svX6F1WohE1XSckf84q-09Q6rj7A |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELZKOcCFN-rSAj7ACazG8SP2ASFey5Y-uLRSTxjbcRYO3Ww3ixD7o_iNzOSxVZHg1ksOTmRZM-P5ZjIef4Q844XnoqgkM55LJq1PzIccEldto9ay0pxjg_PhkZ6cyE-n6nSD_B56YfBY5eATW0dd1hH_ke8KwCklEQ9fz88ZskZhdXWg0OjMYj_9-gkpW_Nq7z3o93mejz8cv5uwnlWARWGyJfM6C7zQPgN4CNryVNmA1SxrpM-kjxHcg0bLLnSKAQBecW1UWdokU0RuXpj3GrkuhbB4hNCMP67t1yh09-vwQMpCSmXXVY2ci5YBmSOFrDJCDk08Ru82XGidMUBMhpTmhq0uAWXLJ3ApCP6rbtvC4fgOudXHsfRNZ3h3yUaa3SO3-5iW9h6juU--fJ7Rpj5LdJrgiXQAdI7__xd4kSutKzqc5abg2mI3NO2uwv6-gpkglV9-O8NOS4qdY029oKAMinCMJvWAnFyJ9B-SzVk9S1uEggZUKb0vYxYgySyMUkGIrPJWVT55PyIvBgG6eXd1h2tTHqNdJ24H4natuN1qRN6ijNdf4rXb7UC9mLp-FzsrMSMLpcpAuzzm3sdc6JDByqQJQo7IzqAh1_uCxl1Y7oi8HLR28frfS3r0_9mekhuT48MDd7B3tL9Nbuat7ViWFztkc7n4kR5DtLQMT1oTpeTrVe-JP0aYH2I |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELZKkRAX3oiFAj7ACayN40fsA6poy9JSKByo1BPGdpyFQzfLZhHq_jR-HTN5bFUkuPWSgxONrJnxPDKe-Qh5xgvPRVFJZjyXTFqfmA85JK7aRq1lpTnHBucPR3r_WL47UScb5PfQC4PXKgeb2Brqso74j3wswE8pif5wXPXXIj7tTbbnPxgiSGGldYDT6FTkMJ39gvSteXWwB7J-nueTN59391mPMMCiMNmSeZ0FXmifgasI2vJU2YCVLWukz6SPEUyFRi0vdIoBnL3i2qiytEmmiDi9QPcKuVoAMURPMJO3a102Ck3_OlSQspBS2XWFI-eiRUPmCCerjJBDQ4_R44YLrTMG3pMhvLlhqwtOs8UWuBAQ_1XDbV3j5Ba50ce09HWnhLfJRprdITf7-Jb21qO5S758nNGmPk10muCJ0AB0jrWABQ51pXVFh3vdFMxc7Jam3Vjs7yugBGn98tspdl1S7CJr6gUFYVB0zahe98jxpXD_Ptmc1bP0gFAphCql92XMAiSchVEqCJFV3qrKJ-9H5MXAQDfvxni4Nv0x2nXsdsBu17LbrUZkB3m8_hJHcLcL9WLq-hPtrMTsLJQqA-nymHsfc6FDBjuTJgg5IluDhFxvFxp3rsUj8nKQ2vnrf2_p4f-pPSXX4DS49wdHh4_I9bxVHcvyYotsLhc_02MInJbhSauhlHy97CPxB8anI48 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+some+geometric+properties+of+sequence+spaces+of+generalized+arithmetic+divisor+sum+function&rft.jtitle=Journal+of+inequalities+and+applications&rft.au=Mursaleen%2C+Mohammad&rft.au=Herawati%2C+Elvina&rft.date=2024-09-27&rft.issn=1029-242X&rft.eissn=1029-242X&rft.volume=2024&rft.issue=1&rft_id=info:doi/10.1186%2Fs13660-024-03208-z&rft.externalDBID=n%2Fa&rft.externalDocID=10_1186_s13660_024_03208_z |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1029-242X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1029-242X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1029-242X&client=summon |