Differential subordinations and superordinations for generalized Bessel functions

TL;DR

This paper explores how differential subordination and superordination properties are preserved for univalent functions in the unit disk when involving an operator with generalized Bessel functions, including special cases with trigonometric functions.

Contribution

It introduces new differential subordination and superordination results for univalent functions using an operator with generalized Bessel functions, extending existing theories.

Findings

Derived preservation properties for univalent functions with generalized Bessel operators

Identified particular cases involving trigonometric functions

Extended classical results to broader function classes

Abstract

Differential subordination and superordination preserving properties for univalent functions in the open unit disk with an operator involving generalized Bessel functions are derived. Some particular cases involving trigonometric functions of our main results are also pointed out.