Investigation of Differential Subordination with the Use of the Generalized Hypergeometric Function

Abstract

The study of analytic univalent and multivalent function theory is an ancient subject of mathematics, particularly in complex analysis, that has drawn a large number of scholars due to the sheer elegance of its geometrical properties and the numerous research opportunities it provides. Researchers have been interested in the traditional study of this subject since at least 1907. During this time, many complex analysis researchers emerged, including Euler, Gauss, Riemann, Cauchy, and many others. Show several results for differential subordination using the convolution operator as well as broader hypergeometric functions. Geometric function theory is a synthesis of geometry and analysis. The main goal of this paper is to investigate the dependence principle and add a new subset for polyvalent functions with a different operator that is related to higher order derivatives. As a result, the discoveries were significant in terms of geometric properties as an example coefficient estimation, growth bounds and distortion, convexity, close to convexity, and the radii of starlikeness.