On Certain Subclasses of Multivalent Analytic Functions with Complex Order Involving a Linear Operator

In the present investigation, we introduce a class 𝓡 p b ( a , c , A , B ) of multivalent analytic functions with complex order, by using a linear operator. For this class, a sufficient condition in terms of the coefficients is obtained, the Fekete–Szegö problem and determination of sharp upper boun...

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Published inVietnam journal of mathematics Vol. 43; no. 3; pp. 645 - 661
Main Authors Sahoo, Ashok Kumar, Patel, Jagannath
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.09.2015
Subjects
Mathematics
Mathematics and Statistics
Saitoh operator
Secondary 33C15
Fekete–Szegö problem
Valent function
Hadamard product
Hankel determinant
Primary 30C45
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Abstract In the present investigation, we introduce a class 𝓡 p b ( a , c , A , B ) of multivalent analytic functions with complex order, by using a linear operator. For this class, a sufficient condition in terms of the coefficients is obtained, the Fekete–Szegö problem and determination of sharp upper bound for the second Hankel determinant is completely solved. We also find the radii of starlikeness and convexity for certain subclass of 𝓡 p b ( a , c , A , B ) . Relevant connections of the results presented here with those obtained in earlier works are pointed out.
AbstractList In the present investigation, we introduce a class 𝓡 p b ( a , c , A , B ) of multivalent analytic functions with complex order, by using a linear operator. For this class, a sufficient condition in terms of the coefficients is obtained, the Fekete–Szegö problem and determination of sharp upper bound for the second Hankel determinant is completely solved. We also find the radii of starlikeness and convexity for certain subclass of 𝓡 p b ( a , c , A , B ) . Relevant connections of the results presented here with those obtained in earlier works are pointed out.
Author Patel, Jagannath
Sahoo, Ashok Kumar
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Cites_doi 10.1090/S0002-9939-1969-0232926-9
10.1137/0515057
10.1007/BF01194100
10.1155/2008/153280
10.1090/S0002-9939-1975-0367176-1
10.1112/jlms/s1-8.2.85
10.1090/S0002-9947-1962-0140674-7
10.2307/2589352
10.1016/S0022-247X(02)00500-0
10.1016/j.jmaa.2006.09.067
10.1090/S0002-9939-1973-0320294-4
10.1090/S0002-9939-1982-0652447-5
10.4064/ap-23-1-73-81
10.5556/j.tkjm.44.2013.963
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Issue 3
Keywords Saitoh operator
Secondary 33C15
Fekete–Szegö problem
Valent function
Hadamard product
Hankel determinant
Primary 30C45
Language English
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References Caplinger, Causey (CR2) 1973; 39
Libera, Złotkiewicz (CR17) 1982; 85
Saitoh (CR31) 1996; 44
Ruscheweyh (CR30) 1975; 49
Juneja, Mogra (CR12) 1979; 103
Makowka (CR22) 1976; 254
MacGregor (CR21) 1962; 104
Choi, Saigo, Srivastava (CR4) 2002; 276
Libera, Zlotkiewicz (CR18) 1983; 87
Fekete, Szegö (CR7) 1933; 8
Mishra, Kund (CR24) 2013; 44
Noor (CR27) 1983; 28
Mishra, Gochhayat (CR23) 2008; 2008
Mogra (CR25) 1981; 4
Carlson, Shaffer (CR3) 1984; 15
Janteng, Halim, Darus (CR10) 2006; 7
Janteng, Halim, Darus (CR11) 2008; 4
Keogh, Merkes (CR13) 1969; 20
Duren (CR5) 1983
Koepf (CR14) 1987; 49
Layman (CR16) 2001; 4
Goel, Sohi (CR8) 1980; 78
Padmanabhan (CR28) 1970; 23
Patel, Mishra (CR29) 2007; 332
Liu, Noor (CR19) 2002; 21
Koepf (CR15) 1987; 101
Ma, Minda, Li, Ren, Yang, Zhang (CR20) 1994
Ahuja (CR1) 1982; 7
Goodman (CR9) 1983
Noonan, Thomas (CR26) 1976; 223
Ehrenborg (CR6) 2000; 107
RJ Libera (120_CR17) 1982; 85
B Makowka (120_CR22) 1976; 254
ML Mogra (120_CR25) 1981; 4
RM Goel (120_CR8) 1980; 78
H Saitoh (120_CR31) 1996; 44
JW Layman (120_CR16) 2001; 4
FR Keogh (120_CR13) 1969; 20
St Ruscheweyh (120_CR30) 1975; 49
KS Padmanabhan (120_CR28) 1970; 23
A Janteng (120_CR11) 2008; 4
KI Noor (120_CR27) 1983; 28
OP Ahuja (120_CR1) 1982; 7
JW Noonan (120_CR26) 1976; 223
AW Goodman (120_CR9) 1983
WC Ma (120_CR20) 1994
J-L Liu (120_CR19) 2002; 21
W Koepf (120_CR14) 1987; 49
J Patel (120_CR29) 2007; 332
AK Mishra (120_CR23) 2008; 2008
AK Mishra (120_CR24) 2013; 44
OP Juneja (120_CR12) 1979; 103
JH Choi (120_CR4) 2002; 276
TR Caplinger (120_CR2) 1973; 39
RJ Libera (120_CR18) 1983; 87
M Fekete (120_CR7) 1933; 8
W Koepf (120_CR15) 1987; 101
TH MacGregor (120_CR21) 1962; 104
BC Carlson (120_CR3) 1984; 15
PL Duren (120_CR5) 1983
R Ehrenborg (120_CR6) 2000; 107
A Janteng (120_CR10) 2006; 7
References_xml – volume: 78
  start-page: 353
  year: 1980
  end-page: 357
  ident: CR8
  article-title: A new criterion for p-valent functions
  publication-title: Proc. Am. Math. Soc.
  contributor:
    fullname: Sohi
– volume: 20
  start-page: 8
  year: 1969
  end-page: 12
  ident: CR13
  article-title: A coefficient inequality for certain classes of analytic functions
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1969-0232926-9
  contributor:
    fullname: Merkes
– volume: 15
  start-page: 737
  year: 1984
  end-page: 745
  ident: CR3
  article-title: Starlike and prestarlike hypergeometric functions
  publication-title: SIAM J. Math. Anal.
  doi: 10.1137/0515057
  contributor:
    fullname: Shaffer
– volume: 44
  start-page: 73
  year: 2013
  end-page: 82
  ident: CR24
  article-title: The second Hankel determinant for a class of analytic functions associated with Carlson–Shaffer operator
  publication-title: Tamkang J. Math.
  contributor:
    fullname: Kund
– volume: 254
  start-page: 71
  year: 1976
  end-page: 76
  ident: CR22
  article-title: On some subclasses of univalent functions
  publication-title: Zesz. Nauk. Polit. Lodzkiejnr
  contributor:
    fullname: Makowka
– volume: 44
  start-page: 31
  year: 1996
  end-page: 38
  ident: CR31
  article-title: A linear operator and its application of first order differential subordinations
  publication-title: Math. Jpn.
  contributor:
    fullname: Saitoh
– volume: 4
  start-page: 1
  year: 2001
  end-page: 11
  ident: CR16
  article-title: The Hankel transform and some of its properties
  publication-title: J. Integer Seq.
  contributor:
    fullname: Layman
– volume: 49
  start-page: 420
  year: 1987
  end-page: 433
  ident: CR14
  article-title: On the Fekete–Szegö problem for close-to-convex functions-II
  publication-title: Arch. Math.
  doi: 10.1007/BF01194100
  contributor:
    fullname: Koepf
– volume: 223
  start-page: 337
  year: 1976
  end-page: 346
  ident: CR26
  article-title: On the second Hankel determinant of areally mean -valent functions
  publication-title: Trans. Am. Math. Soc.
  contributor:
    fullname: Thomas
– volume: 28
  start-page: 731
  year: 1983
  end-page: 739
  ident: CR27
  article-title: Hankel determinant problem for the class of functions with bounded boundary rotation
  publication-title: Rev. Roum. Math. Pures Appl.
  contributor:
    fullname: Noor
– start-page: 157
  year: 1994
  end-page: 169
  ident: CR20
  article-title: A unified treatment of some special classes of univalent functions
  publication-title: Proc. Conf. Complex Anal. (Tianjin, 1992)
  contributor:
    fullname: Zhang
– year: 1983
  ident: CR9
  publication-title: Univalent Functions, vol. I & II
  contributor:
    fullname: Goodman
– volume: 2008
  start-page: 1
  issue: 153280
  year: 2008
  end-page: 10
  ident: CR23
  article-title: Second Hankel determinant for a class of functions defined by fractional derivative
  publication-title: Int. J. Math. Math. Sci.
  doi: 10.1155/2008/153280
  contributor:
    fullname: Gochhayat
– volume: 23
  start-page: 73
  year: 1970
  end-page: 81
  ident: CR28
  article-title: On a certain class of functions whose derivatives have a positive real part in the unit disc
  publication-title: Ann. Polon. Math.
  contributor:
    fullname: Padmanabhan
– volume: 49
  start-page: 109
  year: 1975
  end-page: 115
  ident: CR30
  article-title: New criteria for univalent functions
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1975-0367176-1
  contributor:
    fullname: Ruscheweyh
– volume: 21
  start-page: 81
  year: 2002
  end-page: 90
  ident: CR19
  article-title: Some properties of Noor integral operator
  publication-title: J. Nat. Geom.
  contributor:
    fullname: Noor
– volume: 8
  start-page: 85
  year: 1933
  end-page: 89
  ident: CR7
  article-title: Eine Bemerkung über ungerade schlichte funktionen
  publication-title: J. Lond. Math. Soc.
  doi: 10.1112/jlms/s1-8.2.85
  contributor:
    fullname: Szegö
– volume: 87
  start-page: 251
  year: 1983
  end-page: 257
  ident: CR18
  article-title: Coefficient bounds for the inverse of a function with derivative in 𝓟
  publication-title: Proc. Am. Math. Soc.
  contributor:
    fullname: Zlotkiewicz
– volume: 7
  start-page: 173
  year: 1982
  end-page: 187
  ident: CR1
  article-title: Univalent functions whose derivatives have a positive real part
  publication-title: Rend. Mat.
  contributor:
    fullname: Ahuja
– volume: 101
  start-page: 89
  year: 1987
  end-page: 95
  ident: CR15
  article-title: On the Fekete–Szegö problem for close-to-convex functions
  publication-title: Proc. Am. Math. Soc.
  contributor:
    fullname: Koepf
– volume: 7
  start-page: 5
  issue: 50
  year: 2006
  ident: CR10
  article-title: Coefficient inequality for a function whose derivative has a positive real part
  publication-title: J. Inequal. Pure Appl. Math.
  contributor:
    fullname: Darus
– volume: 104
  start-page: 532
  year: 1962
  end-page: 537
  ident: CR21
  article-title: Functions whose derivative have a positive real part
  publication-title: Trans. Am. Math. Soc.
  doi: 10.1090/S0002-9947-1962-0140674-7
  contributor:
    fullname: MacGregor
– volume: 4
  start-page: 163
  year: 1981
  end-page: 172
  ident: CR25
  article-title: On a class of univalent functions whose derivatives have a positive real part
  publication-title: Riv. Mat. Univ. Parma
  contributor:
    fullname: Mogra
– volume: 107
  start-page: 557
  year: 2000
  end-page: 560
  ident: CR6
  article-title: The Hankel determinant of exponential polynomials
  publication-title: Am. Math. Mon.
  doi: 10.2307/2589352
  contributor:
    fullname: Ehrenborg
– volume: 276
  start-page: 432
  year: 2002
  end-page: 445
  ident: CR4
  article-title: Some inclusion properties of a certain family of integral operators
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/S0022-247X(02)00500-0
  contributor:
    fullname: Srivastava
– volume: 332
  start-page: 109
  year: 2007
  end-page: 122
  ident: CR29
  article-title: On certain subclasses multivalent functions associated with an extended fractional differintegral operator
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2006.09.067
  contributor:
    fullname: Mishra
– volume: 39
  start-page: 357
  year: 1973
  end-page: 361
  ident: CR2
  article-title: A class of univalent functions
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1973-0320294-4
  contributor:
    fullname: Causey
– year: 1983
  ident: CR5
  publication-title: Univalent Functions. Grundlehren der Mathematischen Wissenschaften, vol. 259
  contributor:
    fullname: Duren
– volume: 4
  start-page: 189
  year: 2008
  end-page: 195
  ident: CR11
  article-title: Estimate on the second Hankel functional for functions whose derivative has a positive real part
  publication-title: J. Qual. Meas. Anal.
  contributor:
    fullname: Darus
– volume: 103
  start-page: 435
  year: 1979
  end-page: 447
  ident: CR12
  article-title: A class of univalent functions
  publication-title: Bull. Sci. Sér.
  contributor:
    fullname: Mogra
– volume: 85
  start-page: 225
  year: 1982
  end-page: 230
  ident: CR17
  article-title: Early coefficients of the inverse of a regular convex function
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1982-0652447-5
  contributor:
    fullname: Złotkiewicz
– volume: 23
  start-page: 73
  year: 1970
  ident: 120_CR28
  publication-title: Ann. Polon. Math.
  doi: 10.4064/ap-23-1-73-81
  contributor:
    fullname: KS Padmanabhan
– volume: 44
  start-page: 31
  year: 1996
  ident: 120_CR31
  publication-title: Math. Jpn.
  contributor:
    fullname: H Saitoh
– volume: 39
  start-page: 357
  year: 1973
  ident: 120_CR2
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1973-0320294-4
  contributor:
    fullname: TR Caplinger
– volume: 15
  start-page: 737
  year: 1984
  ident: 120_CR3
  publication-title: SIAM J. Math. Anal.
  doi: 10.1137/0515057
  contributor:
    fullname: BC Carlson
– volume: 4
  start-page: 163
  year: 1981
  ident: 120_CR25
  publication-title: Riv. Mat. Univ. Parma
  contributor:
    fullname: ML Mogra
– volume-title: Univalent Functions, vol. I & II
  year: 1983
  ident: 120_CR9
  contributor:
    fullname: AW Goodman
– volume-title: Univalent Functions. Grundlehren der Mathematischen Wissenschaften, vol. 259
  year: 1983
  ident: 120_CR5
  contributor:
    fullname: PL Duren
– volume: 104
  start-page: 532
  year: 1962
  ident: 120_CR21
  publication-title: Trans. Am. Math. Soc.
  doi: 10.1090/S0002-9947-1962-0140674-7
  contributor:
    fullname: TH MacGregor
– volume: 223
  start-page: 337
  year: 1976
  ident: 120_CR26
  publication-title: Trans. Am. Math. Soc.
  contributor:
    fullname: JW Noonan
– volume: 44
  start-page: 73
  year: 2013
  ident: 120_CR24
  publication-title: Tamkang J. Math.
  doi: 10.5556/j.tkjm.44.2013.963
  contributor:
    fullname: AK Mishra
– volume: 103
  start-page: 435
  year: 1979
  ident: 120_CR12
  publication-title: Bull. Sci. Sér.
  contributor:
    fullname: OP Juneja
– start-page: 157
  volume-title: Proc. Conf. Complex Anal. (Tianjin, 1992)
  year: 1994
  ident: 120_CR20
  contributor:
    fullname: WC Ma
– volume: 107
  start-page: 557
  year: 2000
  ident: 120_CR6
  publication-title: Am. Math. Mon.
  doi: 10.2307/2589352
  contributor:
    fullname: R Ehrenborg
– volume: 49
  start-page: 109
  year: 1975
  ident: 120_CR30
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1975-0367176-1
  contributor:
    fullname: St Ruscheweyh
– volume: 254
  start-page: 71
  year: 1976
  ident: 120_CR22
  publication-title: Zesz. Nauk. Polit. Lodzkiejnr
  contributor:
    fullname: B Makowka
– volume: 276
  start-page: 432
  year: 2002
  ident: 120_CR4
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/S0022-247X(02)00500-0
  contributor:
    fullname: JH Choi
– volume: 8
  start-page: 85
  year: 1933
  ident: 120_CR7
  publication-title: J. Lond. Math. Soc.
  doi: 10.1112/jlms/s1-8.2.85
  contributor:
    fullname: M Fekete
– volume: 78
  start-page: 353
  year: 1980
  ident: 120_CR8
  publication-title: Proc. Am. Math. Soc.
  contributor:
    fullname: RM Goel
– volume: 2008
  start-page: 1
  issue: 153280
  year: 2008
  ident: 120_CR23
  publication-title: Int. J. Math. Math. Sci.
  doi: 10.1155/2008/153280
  contributor:
    fullname: AK Mishra
– volume: 101
  start-page: 89
  year: 1987
  ident: 120_CR15
  publication-title: Proc. Am. Math. Soc.
  contributor:
    fullname: W Koepf
– volume: 87
  start-page: 251
  year: 1983
  ident: 120_CR18
  publication-title: Proc. Am. Math. Soc.
  contributor:
    fullname: RJ Libera
– volume: 21
  start-page: 81
  year: 2002
  ident: 120_CR19
  publication-title: J. Nat. Geom.
  contributor:
    fullname: J-L Liu
– volume: 20
  start-page: 8
  year: 1969
  ident: 120_CR13
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1969-0232926-9
  contributor:
    fullname: FR Keogh
– volume: 7
  start-page: 173
  year: 1982
  ident: 120_CR1
  publication-title: Rend. Mat.
  contributor:
    fullname: OP Ahuja
– volume: 332
  start-page: 109
  year: 2007
  ident: 120_CR29
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2006.09.067
  contributor:
    fullname: J Patel
– volume: 4
  start-page: 189
  year: 2008
  ident: 120_CR11
  publication-title: J. Qual. Meas. Anal.
  contributor:
    fullname: A Janteng
– volume: 28
  start-page: 731
  year: 1983
  ident: 120_CR27
  publication-title: Rev. Roum. Math. Pures Appl.
  contributor:
    fullname: KI Noor
– volume: 7
  start-page: 5
  issue: 50
  year: 2006
  ident: 120_CR10
  publication-title: J. Inequal. Pure Appl. Math.
  contributor:
    fullname: A Janteng
– volume: 4
  start-page: 1
  year: 2001
  ident: 120_CR16
  publication-title: J. Integer Seq.
  contributor:
    fullname: JW Layman
– volume: 49
  start-page: 420
  year: 1987
  ident: 120_CR14
  publication-title: Arch. Math.
  doi: 10.1007/BF01194100
  contributor:
    fullname: W Koepf
– volume: 85
  start-page: 225
  year: 1982
  ident: 120_CR17
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1982-0652447-5
  contributor:
    fullname: RJ Libera
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Snippet In the present investigation, we introduce a class 𝓡 p b ( a , c , A , B ) of multivalent analytic functions with complex order, by using a linear operator....
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SubjectTerms Mathematics
Mathematics and Statistics
Title On Certain Subclasses of Multivalent Analytic Functions with Complex Order Involving a Linear Operator
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