On Kudriasov Conditions for Univalence of Integral Operators Defined by Generalized Bessel Functions

Abstract

In this article, we studied the necessary conditions for the univalence of integral operators that involve two functions: the generalized Bessel function and a function from the well-known class of normalized analytic functions in the open unit disk. The main tools for our discussions were the Kudriasov conditions for the univalency of functions, as well as functional inequalities for the generalized Bessel functions. We included the conditions for the univalency of integral operators that involve Bessel, modified Bessel and spherical Bessel functions as special cases. Furthermore, we provided sufficient conditions for the integral operators that involve trigonometric, as well as hyperbolic, functions as an application of our results.

Geometric Properties of Generalized Integral Operators Related to The Miller–Ross Function

“…Oros [31] studied geometric properties of certain classes of univalent functions using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function. Very recently, Raza et al [32] obtained the necessary conditions for the univalence of integral operators containing the generalized Bessel function. Studies on this subject are still ongoing.…”