Convexity of Certain Integral Operators Defined by Struve Functions

Shahid Mahmood,Sarfraz Nawaz Malik,Sana Mahroz,Mohsan Raza,Ayesha Rafiq

doi:10.1155/2018/6327132

Abstract

This article deals with some functional inequalities involving Struve function, generalized Struve function, and modified Struve functions. We aim to find the convexity of the integral operator defined by Struve function, generalized Struve function, and modified Struve functions.

Highlights

IntroductionLet S∗ and C be the subclasses of S consisting of all functions which map U onto a star shaped with respect to origin and convex domains, respectively
We denote by A the class of functions f which are analytic in the open unit disc U = {z : |z| < 1} and of the form ∞f (z) = z + ∑anzn. (1) n=2Let S denote the class of all functions in A which are univalent in U
We aim to find the convexity of the integral operator defined by Struve function, generalized Struve function, and modified Struve functions

Summary

Introduction

Let S∗ and C be the subclasses of S consisting of all functions which map U onto a star shaped with respect to origin and convex domains, respectively The particular solution of the inhomogeneous equation defined in (6) is called the Struve function of order V. Its particular solution is called the modified Struve functions of order V and is given by LV (z) = −ie−iVπ/2KV (iz). Din et al [10] studied the univalence of integral operators involving generalized Struve functions. These operators are defined as follows: Fα1 ,...,αn ,β [β z.

Main Results

Some Special Cases of Struve Functions and Modified Struve Functions

Locally Univalence Criteria