Fekete-Szeg\"{o} inequality for certain Subclasses of analytic functions related with Crescent-Shaped domain and application of Poison distribution series

Authors

  • Gangadharan Murugusundaramoorthy Dr. G. Murugusundaramoorthy, Ph.D. Professor of Mathematics, SAS Vellore Institute of Technology, Deemed to be University, Vellore- 632 014,India www.vit.ac.in Official Email:gms@vit.ac.in http://orcid.org/0000-0001-8285-6619

DOI:

https://doi.org/10.30495/jme.v0i0.1697

Keywords:

Analytic functions, Starlike functions, Convex functions, Subordination, Fekete-Szeg\"{o} inequality, Poisson distribution series, Hadamard product.

Abstract

The purpose of this paper is to define a newclass of analytic, normalizedfunctions in the open unit disk $\Delta=\{ z:z\in \mathbb{C}\quad \text{and}\quad \left\vertz\right\vert <1\}$ subordinating with crescent shaped regions, and to derive certain  coefficient estimates $a_2$ , $a_3$ and Fekete-Szeg\"{o} inequality for $f\in\mathscr{M}_q(\alpha,\beta,\lambda)$. A similar result have been  done for the function $ f^{-1}. $ Further application of our results to certain functions defined by convolution products with a normalizedanalytic function is given,  in particular we obtainFekete-Szeg\"{o} inequalities for certainsubclasses of functions defined through Poisson distribution series.

Author Biography

Gangadharan Murugusundaramoorthy, Dr. G. Murugusundaramoorthy, Ph.D. Professor of Mathematics, SAS Vellore Institute of Technology, Deemed to be University, Vellore- 632 014,India www.vit.ac.in Official Email:gms@vit.ac.in http://orcid.org/0000-0001-8285-6619

Dr. G. Murugusundaramoorthy, Ph.D.Professor of Mathematics, SASVellore Institute of Technology,Deemed to be University, Vellore- 632 014,India www.vit.ac.inOfficial Email:gms@vit.ac.in
http://orcid.org/0000-0001-8285-6619

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Published

2021-03-24

Issue

Vol. 15

Section

Vol. 15, No. 4, (2021)

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