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Confluent Hypergeometric Distribution and Its Applications on Certain Classes of Univalent Functions of Conic Regions

  • Porwal, Saurabh (Department of Mathematics, UIET, CSJM University)
  • Received : 2016.05.27
  • Accepted : 2018.08.06
  • Published : 2018.09.23

Abstract

The purpose of the present paper is to investigate Confluent hypergeometric distribution. We obtain some basic properties of this distribution. It is worthy to note that the Poisson distribution is a particular case of this distribution. Finally, we give a nice application of this distribution on certain classes of univalent functions of the conic regions.

Keywords

confluent hypergeometric series;univalent functions;starlike functions;convex functions;uniformly convex functions

References

  1. R. Bharati, R Parvatham and A. Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike funcitons, Tamkang J. Math., 28(1997), 17-32.
  2. A. Gangadharan, T. N. Shanmugam and H. M. Srivastava, Generalized hypergeometric function associated with k-uniformly convex functions, Comput. Math. Appl., 44(2002), 1515-1526.
  3. A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56(1991), 87-92. https://doi.org/10.4064/ap-56-1-87-92
  4. 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
  5. 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
  6. 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
  7. S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45(2000), 647-657.
  8. W. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math., 57(1992), 165-175.
  9. S. Ponnusamy and F. Rnning, Starlikeness properties for convolutions involving hypergeometric series, Ann. Univ. Mariae Curie-Sklodawska Sect. A, 52(1998), 141-155.
  10. S. Porwal, An application of a Poisson distribution series on certain analytic functions , J. Complex Anal., (2014), Art. ID 984135, 3 pp
  11. S. Porwal and S. Kumar, Confluent hypergeometric distribution and its applications on certain classes of univalent functions, Afr. Mat., 28(2017), 1-8. https://doi.org/10.1007/s13370-016-0422-3
  12. E. D. Rainville, Special functions, The Macmillan Co., New York, 1960.
  13. M. S. Robertson, On the theory of univalent functions, Ann. Math., 37(1936), 374-408. https://doi.org/10.2307/1968451
  14. F. Rnning, Uniformly convex functions and a corresponding class of starlike functions , Proc. Amer. Math. Soc., 118(1)(1993), 189-196. https://doi.org/10.1090/S0002-9939-1993-1128729-7
  15. H. M. Srivastava and A. K. Mishra, Applications of fractional calculus to parabolic starlike and uniformly convex functions, Comput. Math. Appl., 39(2000), 57-69.
  16. D. Srivastava and S. Porwal, Some sufficient conditions for Poisson distribution series associated with conic regions, Int. J. Advanced Technology in Enginering Sci., 3(1)(2015), 229-236.
  17. A. Swaminathan, Certain sufficiency conditions on Gaussian hypergeometric functions, J. Inequal. Pure Appl. Math., 5(4)(2004), Article 83, 10 pp.