International Journal of Nonlinear Analysis and Applications

An application of the power series distribution for univalent function classes with positive coefficients

Document Type : Research Paper

Authors

1 School of Advanced Sciences, Vellore Institute of Technology, Vellore - 632014, India

2 Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University, Bursa, Turkey

3 Istanbul Gelisim University, Istanbul, Turkey

Abstract

The primary motivation of the paper is to give necessary and sufficient condition for the power series distribution (Pascal model) to be in the subclasses $\mathcal{VS}_{p}\left( \vartheta ,\gamma ,\kappa \right) $ and $\mathcal{VC}_p(\vartheta ,\gamma ,\kappa )$ of analytic functions. Further, to obtain certain connections between the Pascal distribution series and subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 5
May 2023
Pages 259-265
  • Receive Date: 24 February 2021
  • Accept Date: 20 April 2021