Kyungpook Mathematical Journal

  • 제56권2호
  • /
  • Pages.597-610
  • /
  • 2016
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

Some Inclusion Properties of New Subclass of Starlike and Convex Functions associated with Hohlov Operator

  • 투고 : 2014.03.07
  • 심사 : 2015.11.03
  • 발행 : 2016.06.23
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

키워드

참고문헌

  1. L. de Branges, A proof of the Bieberbach conjecture, Acta Math., 154(1985) 137-152. https://doi.org/10.1007/BF02392821
  2. B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15(1984), 737-745. https://doi.org/10.1137/0515057
  3. T. R. Caplinger and W. M. Causey, A class of univalent functions, Proc. Amer. Math. Soc., 39(1973), 357-361. https://doi.org/10.1090/S0002-9939-1973-0320294-4
  4. K. K. Dixit and S. K. Pal, On a class of univalent functions related to complex order, Indian J. Pure Appl. Math., 26(9)(1995), 889-896.
  5. J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103(1999), 1-13. https://doi.org/10.1016/S0377-0427(98)00235-0
  6. J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Intergral Transforms Spec. Funct., 14(2003), 7-18. https://doi.org/10.1080/10652460304543
  7. A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56(1991), 87-92. https://doi.org/10.4064/ap-56-1-87-92
  8. Y. E. Hohlov, Operators and operations in the class of univalent functions, Izv. Vyss. U.cebn. Zaved. Matematika, 10(1978), 83-89.
  9. V. Kiryakova, Criteria for univalence of the Dziok-Srivastava and the Srivastava-Wright operators in the class A, Appl. Math. Comput., 218(3)(2011), 883-892. https://doi.org/10.1016/j.amc.2011.01.076
  10. S. Kanas and H. M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transform Spec. Funct., 9(2000), 121-132. https://doi.org/10.1080/10652460008819249
  11. S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105(1999), 327-336. https://doi.org/10.1016/S0377-0427(99)00018-7
  12. S. Kanas and A. Wisniowska, Conic regions and k-starlike functions, Rev. Roumaine Math. Pures Appl., 45X(2000), 647-657.
  13. K. S. Padmanabhan, On a certain class of functions whose derivatives have a positive real part in the unit disc, Ann. Polon. Math., 23(1970), 73-81. https://doi.org/10.4064/ap-23-1-73-81
  14. S. Ponnusamy and F. Ronning, Duality for Hadamard products applied to certain integral transforms, Complex Variables Theory Appl., 32(1997), 263-287. https://doi.org/10.1080/17476939708814995
  15. H. M. Srivastava, Some Fox-Wright generalized hypergeometric functions and associated families of convolution operators, Appl. Anal. Discrete Math., 1(1)(2007), 56-71. https://doi.org/10.2298/AADM0701056S
  16. H. M. Srivastava, G. Murugusundaramoorthy and S. Sivasubramanian, Hypergeo-metric functions in the parabolic starlike and uniformly convex domains, Integral Transform Spec. Funct., 18(2007), 511-520. https://doi.org/10.1080/10652460701391324