Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Class of Starlike Functions Defined by the Dziok-Srivastava Operator

  • Received : 2007.09.23
  • Accepted : 2008.03.20
  • Published : 2009.03.31
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Abstract

A comprehensive class of starlike univalent functions defined by Dziok-Srivastava operator is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Further distortion bounds, extreme points and results on partial sums are investigated.

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References

  1. B. C. Carlson and S. B. Shaffer, Starlike and prestarlike hypergrometric functions, SIAM J. Math. Anal., 15(2002), 737-745.
  2. B. C. Carlson, Special Functions of Applied Mathematics, Academic Press, New York, 1977.
  3. J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Intergral Transform and Spec. Funct., 14(2003), 7-18. https://doi.org/10.1080/10652460304543
  4. A. W. Goodman, On uniformly convex functions, Ann. polon. Math., 56(1991), 87-92. https://doi.org/10.4064/ap-56-1-87-92
  5. A. W. Goodman, On uniformly starlike functions, J. Math. Anal. & Appl., 155(1991), 364-370. https://doi.org/10.1016/0022-247X(91)90006-L
  6. S. Kanas and H. M. Srivastava, Linear operators associated with k-uniformaly convex functions, Intergral Transform and Spec. Funct., 9(2000), 121-132. https://doi.org/10.1080/10652460008819249
  7. W. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math., 57(1992), 165-175. https://doi.org/10.4064/ap-57-2-165-175
  8. S. Ponnusamy and S. Sabapathy, Geometric properties of generalized hypergeometric functions, Ramanujan Journal, 1(1997), 187-210. https://doi.org/10.1023/A:1009720202474
  9. E. D. Rainville, Special Functions, Chelsea Publishing Company, New York, 1960.
  10. F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1993), 189-196. https://doi.org/10.1090/S0002-9939-1993-1128729-7
  11. F. Ronning, Integral representations for bounded starlike functions, Annal. Polon. Math., 60(1995), 289-297. https://doi.org/10.4064/ap-60-3-289-297
  12. S. Ruscheweyh, New criteria for Univalent Functions, Proc. Amer. Math. Soc., 49(1975), 109-115. https://doi.org/10.1090/S0002-9939-1975-0367176-1
  13. H. Silverman, Univalent functions with varying arguments, Proc. Amer. Math. Soc., 49(1975), 109-115. https://doi.org/10.1090/S0002-9939-1975-0367176-1
  14. H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. & Appl., 209(1997), 221-227. https://doi.org/10.1006/jmaa.1997.5361
  15. E. M. Silvia., Partial sums of convex functions of order $\alpha$, Houston. J. Math., Math. Soc., 11(3)(1985), 397-404.
  16. H. M. Srivastava and S. Owa, Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators and certain subclasses of analytic functions, Nagoya Math. J., 106(1987), 1-28. https://doi.org/10.1017/S0027763000000854
  17. H. M. Srivastava and A. K. Mishra, Applications of fractional calculus to parabolic starlike and uniformly convex functions, Computers Math. Applc., 39(2000), 57-69.
  18. K. G. Subramanian, G. Murugusundaramoorthy, P. Balasubrahmanyam and H. Silverman, Subclasses of uniformly convex and uniformly starlike functions, Math. Japonica., 42(3)(1995), 517-522.
  19. K. Vijaya and G. Murugusundaramoorthy, Some uniformly starlike functions with varying arguments, Tamkang. J. Math., 35(1)(2004), 23-28.