The Principle of Differential Subordination and Its Application to Analytic and p-Valent Functions Defined by a Generalized Fractional Differintegral Operator

Nak Eun Cho,Mohamed Kamal Aouf,Rekha Srivastava

doi:10.3390/sym11091083

Nak Eun Cho, Mohamed Kamal Aouf + Show 1 more

Open Access

https://doi.org/10.3390/sym11091083

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Abstract

A useful family of fractional derivative and integral operators plays a crucial role on the study of mathematics and applied science. In this paper, we introduce an operator defined on the family of analytic functions in the open unit disk by using the generalized fractional derivative and integral operator with convolution. For this operator, we study the subordination-preserving properties and their dual problems. Differential sandwich-type results for this operator are also investigated.

Highlights

The univalent function q (z) is called a dominant of the solutions of Relation (2) if p (z) ≺ q (z) for all p (z) satisfying Relation (2)
The aim of the present paper, motivated by the works mentioned above, is to systematically investigate the subordination- and superordination-preserving results of the generalized fractional differintegral operator defined Equation (7) with certain differential sandwich-type theorems as consequences of the results presented here
Our results give interesting new properties, and together with other papers that appeared in the last years could emphasize the perspective of the importance of differential subordinations and generalized fractional differintegral operators

Summary

Introduction

The univalent function q (z) is called a dominant of the solutions of Relation (2) if p (z) ≺ q (z) for all p (z) satisfying Relation (2). An analytic function q (z) is called a subordinant of the solutions of Relation (3) if q (z) ≺ p (z) for all p (z) satisfying Relation (3). The aim of the present paper, motivated by the works mentioned above, is to systematically investigate the subordination- and superordination-preserving results of the generalized fractional differintegral operator defined Equation (7) with certain differential sandwich-type theorems as consequences of the results presented here.

Results

Conclusion