A Certain Family of Integral Operators Associated with the Struve Functions

Shahid Mahmood,Saira Zainab,Sarfraz Malik,Mohsan Raza,Neelam Shahzadi,H.M Srivastava

doi:10.3390/sym11040463

Abstract

This article presents the study of Struve functions and certain integral operators associated with the Struve functions. It contains the investigation of certain geometric properties like the strong starlikeness and strong convexity of the Struve functions. It also includes the criteria of univalence for a family of certain integral operators associated with the generalized Struve functions. The starlikeness and uniform convexity of the said integral operators are also part of this research.

Highlights

We denote by A the class of functions f that are analytic in the open unit disc D = {z : |z| < 1} and of the form: ∞ f (z) = z + ∑ an zn . (1) n =2 ∼Let S denote the class of all functions in A, which are univalent in D
The particular solution of the inhomogeneous equation defined in Equation (2) is called the Struve function of order L; see [9]
Din et al [14] studied the univalence of integral operators involving generalized Struve functions

Summary

Introduction

The particular solution of the inhomogeneous equation defined in Equation (2) is called the Struve function of order L; see [9]. Din et al [14] studied the univalence of integral operators involving generalized Struve functions. These operators are defined as follows: Fα1 ,...,αn ,β (z) = β. We introduce the following integral operators HLi,b,c,γ1,.., γn ,β , ILi,b,c,γ ,...,γn ,δ,β : A → A involving the generalized Struve functions as: γi β. The starlikeness and uniform convexity of the said integral operators are part of this research

Preliminary Results

Geometric Properties of Generalized Struve Functions

Univalence Criteria for Integral Operators

Starlikeness and Uniform Convexity Criteria for the Integral Operator