On Differential Subordination and Superordination for Univalent Function Involving New Operator

Abstract

The goal of this paper is to explore some of the features of differential subordination of analytic univalent functions in an open unit disc. It also seeks to shed light on geometric features such as coefficient inequality, Hadamard product qualities, and the Komatu integral operator. Some intriguing results for third-order differential subordination and superordination of analytic univalent functions were obtained. Then, using the convolution of two linear operators, certain results of third order differential subordination involving linear operators were reported. We use features of the Komatu integral operator to analyze and study third-order subordinations and superordinations in relation to the convolution. Finally, several results for third order differential subordination in the open unit disk using generalized hypergeometric function were obtained by using the convolution operator