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Differential subordinations and superordinations for generalized Bessel functions

Huda A. Al-Kharsani|\'Arp\'ad Baricz|Kottakkaran S. Nisar
대한수학회 (The Korean Mathematical Society)|2016.01|대한수학회보 (Bulletin of the KMS)|제53권 제1호|pp. 127-138

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키워드

univalent functionsdifferential subordinationdifferential superordinationgeneralized Bessel functionsLoewner chainsandwich type resultsLibera integral operator
주제분류수학

초록

Differential subordination and superordination preserving \linebreak properties for univalent functions in the open unit disk with an operator involving generalized Bessel functions are derived. Some particular cases involving trigonometric functions of our main results are also pointed out.

Abstract

Differential subordination and superordination preserving \linebreak properties for univalent functions in the open unit disk with an operator involving generalized Bessel functions are derived. Some particular cases involving trigonometric functions of our main results are also pointed out.

참고문헌 (16)

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  10. S. S. Miller, "Univalence of Gaussian and confluent hypergeometric functions", Proc. Amer. Math. Soc, 110(2), pp.333~342 (1990)
  11. S. S. Miller, "Differential subordinations, vol. 225 of Monographs and textbooks in Pure and Applied Mathematics" (2000), Marcel Dekker
  12. S. S. Miller, "Subordinants of differential superordinations", Complex Var. Theory Appl, 48(10), pp.815~826 (2003)
  13. S. R.Mondal, "Geometric properties of generalized Bessel functions", Bull. Malays. Math. Sci. Soc., 35(1), pp.179~194 (2012)
  14. S. Ponnusamy, "Geometric properties for convolutions of hypergeometric functions and functions with the derivative in a halfplane", Integral Transform. Spec. Funct, 8(1-2), pp.121~138 (1999)
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  16. S. Ponnusamy, "Univalence and convexity properties for Gaussian hypergeometric functions", Rocky Mountain J. Math, 31(1), pp.327~353 (2001)

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