Generalized Hyers–Ulam stability for general additive functional equations in quasi- β-normed spaces

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers–Ulam stability of Cauchy and Je...

Full description

Saved in:

Bibliographic Details
Published in	Journal of mathematical analysis and applications Vol. 356; no. 1; pp. 302 - 309
Main Authors	Rassias, John Michael, Kim, Hark-Mahn
Format	Journal Article
Language	English
Published	Amsterdam Elsevier Inc 01.08.2009 Elsevier
Subjects	( [formula omitted])-Banach spaces Contractively subadditive Difference and functional equations, recurrence relations Exact sciences and technology Expansively superadditive Finite differences and functional equations Functional analysis Generalized Hyers–Ulam stability Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Quasi- β-normed spaces Sciences and techniques of general use Contractively subadditive Expansively superadditive ( β , p )-Banach spaces Quasi- β-normed spaces Generalized Hyers–Ulam stability Functional Generalized Hyers-Ulam stability (β, p)-Banach spaces Mathematical analysis Functional equation Banach space Quasi-β-normed spaces Application Numerical stability
Online Access	Get full text

Cover

Loading…

Abstract	In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers–Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers–Ulam stability for general additive functional equations in quasi- β-normed spaces.
AbstractList	In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers–Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers–Ulam stability for general additive functional equations in quasi- β-normed spaces.
Author	Rassias, John Michael Kim, Hark-Mahn
Author_xml	– sequence: 1 givenname: John Michael surname: Rassias fullname: Rassias, John Michael email: jrassias@primedu.uoa.gr organization: Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, Agamemnonos St., Aghia Paraskevi, Athens 15342, Greece – sequence: 2 givenname: Hark-Mahn surname: Kim fullname: Kim, Hark-Mahn email: hmkim@cnu.ac.kr, hmkim@math.cnu.ac.kr organization: Department of Mathematics, Chungnam National University, 220 Yuseong-Gu, Daejeon 305-764, Republic of Korea
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21520458$$DView record in Pascal Francis
BookMark	eNp9kMtKAzEUhoNUsF5ewFU2Lmc8yVwLbqR4A8GNgrtwJjmRlGmmJlOhrnwH38QH8SF8EqdWNy66Ohf-74f_32cj33li7FhAKkCUp7N0NkdMJcAkhSwFKHbYWMCkTKAW2YiNAaRMZF497rH9GGcAQhSVGLOnK_IUsHWvZPj1ikL8ent_aHHOY4-Na12_4rYL_Gkj42iM690Lcbv0unedH370vMT1GrnzfNijS_jnR-K7MB9M4wI1xUO2a7GNdPQ7D9jD5cX99Dq5vbu6mZ7fJjrLoE9ETVZDbYwVoixKasqyrAqQTdYYg3UNw5mL3Fa2NCgJdINSTqoitw0WtZhkB-xk47vAqLG1Ab12US2Cm2NYKSkKCXlRD7p6o9OhizGQVdr1Pyn6gK5VAtS6WDVT62LVulgFmRqKHVD5D_1z3wqdbSAawr84CipqR16TcYF0r0zntuHfPmCXKQ
CODEN	JMANAK
CitedBy_id	crossref_primary_10_1515_tmj_2016_0008 crossref_primary_10_26637_mjm101_002 crossref_primary_10_1155_2010_423231 crossref_primary_10_1155_2010_198098 crossref_primary_10_1186_1029_242X_2012_186 crossref_primary_10_3390_math10101704 crossref_primary_10_1155_2022_9908530 crossref_primary_10_32513_tbilisi_1569463242 crossref_primary_10_4134_BKMS_2013_50_6_2061 crossref_primary_10_1186_1029_242X_2013_71 crossref_primary_10_1007_s13398_021_01111_6 crossref_primary_10_3390_sym14081700 crossref_primary_10_1016_j_jmaa_2018_06_024 crossref_primary_10_4236_apm_2016_612070 crossref_primary_10_26637_MJM0601_0022 crossref_primary_10_1007_s13398_018_0506_z crossref_primary_10_14403_jcms_2016_29_2_287 crossref_primary_10_1007_s00009_010_0082_8 crossref_primary_10_1007_s10114_011_0179_4 crossref_primary_10_1155_2010_635720 crossref_primary_10_1155_2010_368981 crossref_primary_10_1142_S1793557111000332 crossref_primary_10_1155_2012_219435 crossref_primary_10_1186_1029_242X_2013_88 crossref_primary_10_1007_s40065_017_0186_0 crossref_primary_10_1007_s10114_010_9330_x crossref_primary_10_1186_1687_1847_2012_98 crossref_primary_10_5269_bspm_43662 crossref_primary_10_1088_1742_6596_1377_1_012011 crossref_primary_10_1007_s11228_010_0153_9 crossref_primary_10_3390_sym14040700 crossref_primary_10_1016_j_jmaa_2016_10_063 crossref_primary_10_26637_MJM0601_0030 crossref_primary_10_1155_2010_184542 crossref_primary_10_26637_mjm202_003 crossref_primary_10_3233_JIFS_16460 crossref_primary_10_1063_1_4803026 crossref_primary_10_1155_2020_6678772 crossref_primary_10_4236_am_2019_1010058 crossref_primary_10_26637_mjm502_003 crossref_primary_10_1007_s11784_016_0317_9 crossref_primary_10_14403_jcms_2013_26_4_757 crossref_primary_10_1155_2012_896032 crossref_primary_10_1007_s00010_019_00665_6 crossref_primary_10_3390_math12182868 crossref_primary_10_1016_j_jmaa_2009_08_021 crossref_primary_10_26637_mjm501_008 crossref_primary_10_4134_BKMS_2014_51_5_1511 crossref_primary_10_14403_jcms_2015_28_2_311 crossref_primary_10_1155_2021_5577833 crossref_primary_10_1016_j_jmaa_2012_04_086 crossref_primary_10_1186_1029_242X_2013_166 crossref_primary_10_1186_1687_1847_2013_203
Cites_doi	10.1090/S0002-9939-1978-0507327-1 10.1006/jmaa.1999.6546 10.4064/ap83-3-6 10.2969/jmsj/00210064 10.1016/j.bulsci.2005.02.001 10.1006/jmaa.1994.1211 10.1016/S0022-247X(03)00136-7 10.1016/0021-9045(92)90140-J 10.1090/S0002-9939-1992-1059634-1 10.1016/j.jmaa.2007.09.025 10.1090/S0002-9904-1951-09511-7 10.1090/S0002-9947-1978-0511409-2 10.1073/pnas.27.4.222 10.1016/j.bulsci.2006.03.011 10.1016/0021-9045(89)90041-5 10.1155/S016117129100056X
ContentType	Journal Article
Copyright	2009 Elsevier Inc. 2009 INIST-CNRS
Copyright_xml	– notice: 2009 Elsevier Inc. – notice: 2009 INIST-CNRS
DBID	6I. AAFTH AAYXX CITATION IQODW
DOI	10.1016/j.jmaa.2009.03.005
DatabaseName	ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef Pascal-Francis
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Mathematics
EISSN	1096-0813
EndPage	309
ExternalDocumentID	21520458 10_1016_j_jmaa_2009_03_005 S0022247X09002017
GroupedDBID	--K --M --Z -~X .~1 0R~ 0SF 1B1 1RT 1~. 1~5 29L 4.4 457 4G. 5GY 5VS 6I. 6TJ 7-5 71M 85S 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AASFE AAXUO ABAOU ABEFU ABFNM ABJNI ABMAC ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADFGL ADIYS ADMUD AEBSH AEKER AENEX AETEA AEXQZ AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AI. AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CAG COF CS3 DM4 EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA HVGLF HZ~ H~9 IHE IXB J1W KOM LG5 M25 M41 MCRUF MHUIS MO0 MVM N9A NCXOZ O-L O9- OAUVE OHT OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K TN5 TWZ UPT VH1 VOH WH7 WUQ XOL XPP YQT YYP ZCG ZMT ZU3 ~G- AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACRPL ACVFH ADCNI ADNMO ADVLN ADXHL AEIPS AEUPX AFJKZ AFPUW AFXIZ AGCQF AGQPQ AGRNS AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP BNPGV CITATION SSH EFKBS IQODW
ID	FETCH-LOGICAL-c330t-18efc08ddf11656eb6667502b3bdda880667414f7f6da2e0cba229754fba58193
IEDL.DBID	.~1
ISSN	0022-247X
IngestDate	Mon Jul 21 09:14:04 EDT 2025 Tue Jul 01 01:38:36 EDT 2025 Thu Apr 24 23:03:58 EDT 2025 Fri Feb 23 02:27:53 EST 2024
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Contractively subadditive Expansively superadditive ( β , p )-Banach spaces Quasi- β-normed spaces Generalized Hyers–Ulam stability Functional Generalized Hyers-Ulam stability (β, p)-Banach spaces Mathematical analysis Functional equation Banach space Quasi-β-normed spaces Application Numerical stability
Language	English
License	http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 CC BY 4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c330t-18efc08ddf11656eb6667502b3bdda880667414f7f6da2e0cba229754fba58193
OpenAccessLink	https://www.sciencedirect.com/science/article/pii/S0022247X09002017
PageCount	8
ParticipantIDs	pascalfrancis_primary_21520458 crossref_citationtrail_10_1016_j_jmaa_2009_03_005 crossref_primary_10_1016_j_jmaa_2009_03_005 elsevier_sciencedirect_doi_10_1016_j_jmaa_2009_03_005
ProviderPackageCode	CITATION AAYXX
PublicationCentury	2000
PublicationDate	2009-08-01
PublicationDateYYYYMMDD	2009-08-01
PublicationDate_xml	– month: 08 year: 2009 text: 2009-08-01 day: 01
PublicationDecade	2000
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Journal of mathematical analysis and applications
PublicationYear	2009
Publisher	Elsevier Inc Elsevier
Publisher_xml	– name: Elsevier Inc – name: Elsevier
References	Zhou (bib022) 1992; 69 Hyers (bib009) 1941; 27 Rolewicz (bib019) 1984 Benyamini, Lindenstrauss (bib002) 2000; vol. 48 Gǎvruta (bib006) 1994; 184 Rassias, Rassias (bib014) 2003; 281 Tabor (bib020) 2004; 83 Aoki (bib001) 1950; 2 Gajda (bib004) 1991; 14 Rassias, Šemrl (bib018) 1992; 114 Malliavin (bib011) 1997 Najati, Ranjbari (bib012) 2008; 341 Lee, Jun (bib010) 1999; 238 Gǎvruta (bib007) 1999 Rassias, Rassias (bib015) 2005; 129 Rassias (bib016) 2007; 131 Gruber (bib008) 1978; 245 Rassias (bib013) 1989; 57 Gajda, Ger (bib005) 1987; vol. 80 Ulam, Ulam (bib021) 1960 Rassias (bib017) 1978; 72 Bourgin (bib003) 1951; 57 Rassias (10.1016/j.jmaa.2009.03.005_bib017) 1978; 72 Rassias (10.1016/j.jmaa.2009.03.005_bib016) 2007; 131 Lee (10.1016/j.jmaa.2009.03.005_bib010) 1999; 238 Rassias (10.1016/j.jmaa.2009.03.005_bib015) 2005; 129 Rassias (10.1016/j.jmaa.2009.03.005_bib014) 2003; 281 Tabor (10.1016/j.jmaa.2009.03.005_bib020) 2004; 83 Malliavin (10.1016/j.jmaa.2009.03.005_bib011) 1997 Ulam (10.1016/j.jmaa.2009.03.005_bib021_1) 1960 Benyamini (10.1016/j.jmaa.2009.03.005_bib002) 2000; vol. 48 Hyers (10.1016/j.jmaa.2009.03.005_bib009) 1941; 27 Gajda (10.1016/j.jmaa.2009.03.005_bib005) 1987; vol. 80 Rassias (10.1016/j.jmaa.2009.03.005_bib018) 1992; 114 Najati (10.1016/j.jmaa.2009.03.005_bib012) 2008; 341 Rassias (10.1016/j.jmaa.2009.03.005_bib013) 1989; 57 Rolewicz (10.1016/j.jmaa.2009.03.005_bib019) 1984 Zhou (10.1016/j.jmaa.2009.03.005_bib022) 1992; 69 Gajda (10.1016/j.jmaa.2009.03.005_bib004) 1991; 14 Bourgin (10.1016/j.jmaa.2009.03.005_bib003) 1951; 57 Gǎvruta (10.1016/j.jmaa.2009.03.005_bib006) 1994; 184 Aoki (10.1016/j.jmaa.2009.03.005_bib001) 1950; 2 Gǎvruta (10.1016/j.jmaa.2009.03.005_bib007) 1999 Gruber (10.1016/j.jmaa.2009.03.005_bib008) 1978; 245 Ulam (10.1016/j.jmaa.2009.03.005_bib021_2) 1964
References_xml	– volume: 69 start-page: 167 year: 1992 end-page: 172 ident: bib022 article-title: On a conjecture of Z. Ditzian publication-title: J. Approx. Theory – volume: 131 start-page: 89 year: 2007 end-page: 98 ident: bib016 article-title: Refined Hyers–Ulam approximation of approximately Jensen type mappings publication-title: Bull. Sci. Math. – start-page: 67 year: 1999 end-page: 71 ident: bib007 article-title: An answer to a question of John M. Rassias concerning the stability of Cauchy equation publication-title: Advances in Equations and Inequalities – volume: 14 start-page: 431 year: 1991 end-page: 434 ident: bib004 article-title: On stability of additive mappings publication-title: Int. J. Math. Math. Sci. – year: 1960 ident: bib021 article-title: A collection of Mathematical Problems – volume: 72 start-page: 297 year: 1978 end-page: 300 ident: bib017 article-title: On the stability of the linear mapping in Banach spaces publication-title: Proc. Amer. Math. Soc. – volume: 83 start-page: 243 year: 2004 end-page: 255 ident: bib020 article-title: Stability of the Cauchy functional equation in quasi-Banach spaces publication-title: Ann. Polon. Math. – volume: vol. 80 year: 1987 ident: bib005 article-title: Subadditive multifunctions and Hyers–Ulam stability publication-title: General Inequalities, vol. 5 – volume: 281 start-page: 516 year: 2003 end-page: 524 ident: bib014 article-title: On the Ulam stability of Jensen and Jensen type mappings on restricted domains publication-title: J. Math. Anal. Appl. – volume: 129 start-page: 545 year: 2005 end-page: 558 ident: bib015 article-title: Asymptotic behavior of alternative Jensen and Jensen type functional equations publication-title: Bull. Sci. Math. – volume: 57 start-page: 223 year: 1951 end-page: 237 ident: bib003 article-title: Classes of transformations and bordering transformations publication-title: Bull. Amer. Math. Soc. – volume: 341 start-page: 62 year: 2008 end-page: 79 ident: bib012 article-title: Stability of homomorphisms for a 3D Cauchy–Jensen type functional equation on publication-title: J. Math. Anal. Appl. – volume: 27 start-page: 222 year: 1941 end-page: 224 ident: bib009 article-title: On the stability of the linear functional equation publication-title: Proc. Natl. Acad. Sci. – volume: 245 start-page: 263 year: 1978 end-page: 277 ident: bib008 article-title: Stability of isometries publication-title: Trans. Amer. Math. Soc. – volume: 238 start-page: 305 year: 1999 end-page: 315 ident: bib010 article-title: A generalization of the Hyers–Ulam–Rassias stability of Jensen's equation publication-title: J. Math. Anal. Appl. – volume: vol. 48 year: 2000 ident: bib002 article-title: Geometric Nonlinear Functional Analysis, vol. 1 publication-title: Colloq. Publ. – volume: 184 start-page: 431 year: 1994 end-page: 436 ident: bib006 article-title: A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings publication-title: J. Math. Anal. Appl. – year: 1997 ident: bib011 article-title: Stochastic Analysis – volume: 114 start-page: 989 year: 1992 end-page: 993 ident: bib018 article-title: On the behaviour of mappings which do not satisfy Hyers–Ulam stability publication-title: Proc. Amer. Math. Soc. – year: 1984 ident: bib019 article-title: Metric Linear Spaces – volume: 2 start-page: 64 year: 1950 end-page: 66 ident: bib001 article-title: On the stability of the linear transformation in Banach spaces publication-title: J. Math. Soc. Japan – volume: 57 start-page: 268 year: 1989 end-page: 273 ident: bib013 article-title: Solution of a problem of Ulam publication-title: J. Approx. Theory – volume: vol. 48 year: 2000 ident: 10.1016/j.jmaa.2009.03.005_bib002 article-title: Geometric Nonlinear Functional Analysis, vol. 1 – volume: 72 start-page: 297 year: 1978 ident: 10.1016/j.jmaa.2009.03.005_bib017 article-title: On the stability of the linear mapping in Banach spaces publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1978-0507327-1 – year: 1960 ident: 10.1016/j.jmaa.2009.03.005_bib021_1 – volume: 238 start-page: 305 year: 1999 ident: 10.1016/j.jmaa.2009.03.005_bib010 article-title: A generalization of the Hyers–Ulam–Rassias stability of Jensen's equation publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1999.6546 – start-page: 67 year: 1999 ident: 10.1016/j.jmaa.2009.03.005_bib007 article-title: An answer to a question of John M. Rassias concerning the stability of Cauchy equation – volume: vol. 80 year: 1987 ident: 10.1016/j.jmaa.2009.03.005_bib005 article-title: Subadditive multifunctions and Hyers–Ulam stability – volume: 83 start-page: 243 year: 2004 ident: 10.1016/j.jmaa.2009.03.005_bib020 article-title: Stability of the Cauchy functional equation in quasi-Banach spaces publication-title: Ann. Polon. Math. doi: 10.4064/ap83-3-6 – year: 1984 ident: 10.1016/j.jmaa.2009.03.005_bib019 – volume: 2 start-page: 64 year: 1950 ident: 10.1016/j.jmaa.2009.03.005_bib001 article-title: On the stability of the linear transformation in Banach spaces publication-title: J. Math. Soc. Japan doi: 10.2969/jmsj/00210064 – volume: 129 start-page: 545 year: 2005 ident: 10.1016/j.jmaa.2009.03.005_bib015 article-title: Asymptotic behavior of alternative Jensen and Jensen type functional equations publication-title: Bull. Sci. Math. doi: 10.1016/j.bulsci.2005.02.001 – volume: 184 start-page: 431 year: 1994 ident: 10.1016/j.jmaa.2009.03.005_bib006 article-title: A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1994.1211 – year: 1997 ident: 10.1016/j.jmaa.2009.03.005_bib011 – volume: 281 start-page: 516 year: 2003 ident: 10.1016/j.jmaa.2009.03.005_bib014 article-title: On the Ulam stability of Jensen and Jensen type mappings on restricted domains publication-title: J. Math. Anal. Appl. doi: 10.1016/S0022-247X(03)00136-7 – volume: 69 start-page: 167 year: 1992 ident: 10.1016/j.jmaa.2009.03.005_bib022 article-title: On a conjecture of Z. Ditzian publication-title: J. Approx. Theory doi: 10.1016/0021-9045(92)90140-J – volume: 114 start-page: 989 year: 1992 ident: 10.1016/j.jmaa.2009.03.005_bib018 article-title: On the behaviour of mappings which do not satisfy Hyers–Ulam stability publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1992-1059634-1 – volume: 341 start-page: 62 year: 2008 ident: 10.1016/j.jmaa.2009.03.005_bib012 article-title: Stability of homomorphisms for a 3D Cauchy–Jensen type functional equation on C∗-ternary algebras publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2007.09.025 – volume: 57 start-page: 223 year: 1951 ident: 10.1016/j.jmaa.2009.03.005_bib003 article-title: Classes of transformations and bordering transformations publication-title: Bull. Amer. Math. Soc. doi: 10.1090/S0002-9904-1951-09511-7 – volume: 245 start-page: 263 year: 1978 ident: 10.1016/j.jmaa.2009.03.005_bib008 article-title: Stability of isometries publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-1978-0511409-2 – year: 1964 ident: 10.1016/j.jmaa.2009.03.005_bib021_2 – volume: 27 start-page: 222 year: 1941 ident: 10.1016/j.jmaa.2009.03.005_bib009 article-title: On the stability of the linear functional equation publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.27.4.222 – volume: 131 start-page: 89 year: 2007 ident: 10.1016/j.jmaa.2009.03.005_bib016 article-title: Refined Hyers–Ulam approximation of approximately Jensen type mappings publication-title: Bull. Sci. Math. doi: 10.1016/j.bulsci.2006.03.011 – volume: 57 start-page: 268 year: 1989 ident: 10.1016/j.jmaa.2009.03.005_bib013 article-title: Solution of a problem of Ulam publication-title: J. Approx. Theory doi: 10.1016/0021-9045(89)90041-5 – volume: 14 start-page: 431 year: 1991 ident: 10.1016/j.jmaa.2009.03.005_bib004 article-title: On stability of additive mappings publication-title: Int. J. Math. Math. Sci. doi: 10.1155/S016117129100056X
SSID	ssj0011571
Score	2.2086635
Snippet	In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to...
SourceID	pascalfrancis crossref elsevier
SourceType	Index Database Enrichment Source Publisher
StartPage	302
SubjectTerms	( [formula omitted])-Banach spaces Contractively subadditive Difference and functional equations, recurrence relations Exact sciences and technology Expansively superadditive Finite differences and functional equations Functional analysis Generalized Hyers–Ulam stability Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Quasi- β-normed spaces Sciences and techniques of general use
Title	Generalized Hyers–Ulam stability for general additive functional equations in quasi- β-normed spaces
URI	https://dx.doi.org/10.1016/j.jmaa.2009.03.005
Volume	356
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
link	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV29TsMwELZQWUAI8SvKT-WBDRmS2MHNCBVVC4KJSt0iO7GrVBAKLQMMiHfgTXgQHoIn4a52KhhgYIujsxOd7bsv8d13hOzrRFrNQ850M4uZEEYzBcCcySRTxioec4v5zpdXx52eOO_H_TnSqnJhMKzS235n06fW2t858to8GhUF5viCbxOyHySIeULMKBdC4io_fJmFeSCXTFgxhqO0T5xxMV7DW6U8ZyUSnca_OaelkRqDyqyrdfHNAbVXyLJHjvTEvdwqmTPlGlm8nNGujtfJwJNIF88mpx0E05-vbz2YcwoYcBoF-0QBpNKBE6MYTITmjqJ3cz8Fqbl35N9jWpQUrscFox_vrARsC4OC_QHDskF67bPrVof5Sgos4zyYsLBpbBY089xO2XaMho8WgAqR5jrPFWxhaIpQWGmPcxWZINMqwpRbYbWKATPwTVIr70qzRaiCTRtKncvYSJFFAcArnidSqRChSRDVSVipMM08zThWu7hJq3iyYYpqx_qXSRrwFNReJwezPiNHsvGndFzNTPpjqaTgBf7s1_gxjbNHYWlfPC_e_ufAO2TBnTFhWOAuqU0eHs0eQJWJbkzXYoPMn3QvOlfQ6vZPvwCz1evt
linkProvider	Elsevier
linkToHtml	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV29TsMwELYKDIAQ4lf8Fg9syJDEDm5GhEAFWiYqdYvsxEZBEAotAwyId-BNeBAegifhrnYqOsDAlkR2Ep3tuy_xd98RsqsTaTUPOdONLGZCGM0UAHMmk0wZq3jMLeY7ty8Pmx1x3o27NXJc5cIgrdL7fufTh97aXznw1jzoFQXm-EJsE7IbJIh5QjlBpgQsXyxjsP864nmgmExYSYZjc58540heN3dKedFKVDqNf4tOcz3VB5tZV-ziRwQ6XSDzHjrSI_d2i6RmyiUy2x7prvaXybVXkS5eTE6biKa_3t47MOgUQOCQBvtMAaXSa9eMIpsI_R3F8Ob-ClLz4NS_-7QoKRz3C0Y_P1gJ4BZuCg4IPMsK6ZyeXB03mS-lwDLOgwELG8ZmQSPP7VBux2j4agGsEGmu81zBGoZTEQor7WGuIhNkWkWYcyusVjGABr5KJsv70qwRqmDVhlLnMjZSZFEA-IrniVQqRGwSROskrEyYZl5nHMtd3KYVoewmRbNjAcwkDXgKZl8ne6M-Paey8WfruBqZdGyupBAG_uxXHxvG0aOwti9uGG_888Y7ZLp51W6lrbPLi00y4zackCO4RSYHj09mG3DLQNeH8_IbmEnsdw
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=Generalized+Hyers%E2%80%93Ulam+stability+for+general+additive+functional+equations+in+quasi-+%CE%B2-normed+spaces&rft.jtitle=Journal+of+mathematical+analysis+and+applications&rft.au=Rassias%2C+John+Michael&rft.au=Kim%2C+Hark-Mahn&rft.date=2009-08-01&rft.pub=Elsevier+Inc&rft.issn=0022-247X&rft.eissn=1096-0813&rft.volume=356&rft.issue=1&rft.spage=302&rft.epage=309&rft_id=info:doi/10.1016%2Fj.jmaa.2009.03.005&rft.externalDocID=S0022247X09002017
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-247X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-247X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-247X&client=summon