Korean J. Math. Vol. 24 No. 2 (2016) pp.139-168
DOI: https://doi.org/10.11568/kjm.2016.24.2.139

Inclusion properties of a class of functions involving the Dziok-Srivastava operator

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Published: Jun 30, 2016
Keywords:
Analytic functions, Starlike and uniformly starlike functions with respect to symmetric points, Generalized hypergeometric functions, Dziok- Srivastava linear operator, Coefficient estimates, Srivastava-Wright operator, Integral transforms, Komatu operato
Mathematics Subject Classification:
30C45, 30C80.

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Satwanti Devi
Department of Mathematics Indian Institute of Technology Roorkee 247 667 Uttarakhand, India
H. M. Srivastava
Department of Mathematics and Statistics University of Victoria Victoria, British Columbia V8W 3P4, Canada
A. Swaminathan
Department of Mathematics Indian Institute of Technology Roorkee 247 667 Uttarakhand, India

Abstract

In this work, we first introduce a class of analytic functions involving the Dziok-Srivastava linear operator that generalizes the class of uniformly starlike functions with respect to symmetric points. We then establish the closure of certain well-known integral transforms under this analytic function class. This behaviour leads to various radius results for these integral transforms. Some of the interesting consequences of these results are outlined. Further, the lower bounds for the ratio between the functions $f(z)$ in the class under discussion, their partial sums $f_m(z)$ and the corresponding derivative functions $f'(z)$ and $f'_m(z)$ are determined by using the coefficient estimates.


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