Kyungpook Mathematical Journal

  • 제46권1호
  • /
  • Pages.97-109
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  • 2006
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

Classes of Multivalent Functions Defined by Dziok-Srivastava Linear Operator and Multiplier Transformation

  • Kumar, S. Sivaprasad (Department of Applied Mathematics, Delhi College of Engineering) ;
  • Taneja, H.C. (Department of Applied Mathematics, Delhi College of Engineering) ;
  • Ravichandran, V. (School of Mathematical Sciences, Universiti Sains Malaysia)
  • 투고 : 2004.09.30
  • 발행 : 2006.03.23
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초록

In this paper, the authors introduce new classes of p-valent functions defined by Dziok-Srivastava linear operator and the multiplier transformation and study their properties by using certain first order differential subordination and superordination. Also certain inclusion relations are established and an integral transform is discussed.

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참고문헌

  1. S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135(1969), 429-446. https://doi.org/10.1090/S0002-9947-1969-0232920-2
  2. T. Bulboaca, A class of superordination-preserving integral operators, Indag. Math. (N.S.), 13(3)(2002), 301-311. https://doi.org/10.1016/S0019-3577(02)80013-1
  3. T. Bulboaca, Classes of first-order differential superordinations, Demonstratio Math., 35(2)(2002), 287-292.
  4. B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15(4)(1984), 737-745. https://doi.org/10.1137/0515057
  5. N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling, 37(1- 2)(2003), 39-49. https://doi.org/10.1016/S0895-7177(03)80004-3
  6. N. E. Cho and T. H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc., 40(3)(2003), 399-410. https://doi.org/10.4134/BKMS.2003.40.3.399
  7. J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14(1)(2003), 7-18. https://doi.org/10.1080/10652460304543
  8. Ju. E. Hohlov, Operators and operations on the class of univalent functions, Izv. Vyssh. Uchebn. Zaved. Mat. 1978, 10(197)(1978), 83-89.
  9. R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16(1965), 755-758. https://doi.org/10.1090/S0002-9939-1965-0178131-2
  10. J.-L. Liu and S. Owa, On a class of multivalent functions involving certain linear operator, Indian J. Pure Appl. Math., 33(11)(2002), 1713-1722.
  11. A. E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc., 17(1966), 352-357. https://doi.org/10.1090/S0002-9939-1966-0188423-X
  12. S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Monographs and Textbooks in Pure and Applied Mathematics, No. 225, Marcel Dekker, New York, (2000).
  13. S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Var. Theory Appl., 48(10)(2003), 815-826. https://doi.org/10.1080/02781070310001599322
  14. S. Owa, On the distortion theorems I, Kyungpook Math. J., 18(1)(1978), 53-59.
  15. S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39(5)(1987), 1057-1077. https://doi.org/10.4153/CJM-1987-054-3
  16. St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109-115. https://doi.org/10.1090/S0002-9939-1975-0367176-1
  17. G. S. Salagean, Subclasses of univalent functions, in Complex analysis—fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math., 1013, Springer, Berlin.
  18. H. M. Srivastava, Some families of fractional derivative and other linear operators associated with analytic, univalent, and multivalent functions, in Analysis and its applications (Chennai, 2000), 209-243, Allied Publ., New Delhi.
  19. B. A. Uralegaddi and C. Somanatha, Certain classes of univalent functions, in Current topics in analytic function theory, 371-374, World Sci. Publishing, River Edge, NJ, (1992).