Title: Application of Hypergeometric Distribution Series on Certain Subclass of Analytic Functions
Author(s): Trailokya Panigrahi
Pages: 157-162
Cite as:
Trailokya Panigrahi, Application of Hypergeometric Distribution Series on Certain Subclass of Analytic Functions, Int. J. Anal. Appl., 12 (2) (2016), 157-162.


The object of the present paper is to give some characterizations for hypergeometric distribution series to be in various subclasses of analytic functions.

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  1. M. K. Aouf, On certain subclass of analytic p-valent functions of order alpha, Rend. Mat., 7(8) (1988), 89-104.

  2. M. K. Aouf, A. O. Mostafa and H. M. Zayed, Some constraints of hypergeometric functions to belong to certain subclasses of analytic functions, J. Egyptian Math. Soc., 24(3) (2016), 361-366.

  3. P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Vol 259, Springer-Verlag, New York, 1983.

  4. A. W. Goodman, On uniformly convex functions, Ann. Polon. Math, 56(1)(1991), 87-92.

  5. S. Kanas and A. Wisnioska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105(1999), 327-336.

  6. S. Kanas and A. Wisnioska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45(4) (2000), 647-657.

  7. W. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math., 57(2) (1992), 165-175.

  8. S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, in: Monographs and Text Books in Pure and Applied Mathematics, 225, Marcel Dekker, New York, 2000.

  9. A. K. Mishra and T. Panigrahi, Class-mapping properties of the Hohlov operator, Bull. Korean Math. Soc., 48(1) (2011), 51-65.

  10. S. Ponnusamy and F. Ronning, Starlikeness properties for convolution involving hypergeometric series, Ann. Univ. Mariae Curie-Sklodowska I, II 1(16) (1998), 141-155.

  11. S. Porwal and S. Kumar, Confluent hypergeometric distribution and its applications on certain classes of univalent functions, Afr. Mat., (2016), doi:10.1007/s13370-016-0422-3.

  12. F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1) (1993), 189-196.

  13. A. K. Sharma, S. Porwal and K. K. Dixit , Class-mapping properties of convolution involving certain univalent function associated with hypergeometric function, Electronic J. Math. Anal. Appl., 1(2) (2013), 326-333.