Strong Differential Subordinations Obtained with New Integral Operator Defined by Polylogarithm Function

K Al-Shaqsi

doi:10.1155/2014/260198

Abstract

By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.

Highlights

Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions
Let H denote the class of analytic function in the open unit disk U = {z : |z| < 1}
In the present paper, making use of polylogarithm function, we introduce a new integral operator

Summary

Introduction

Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions. If p(z) is analytic in U and satisfies the (second-order) differential subordination φ (p (z) , zp󸀠 (z) , zp󸀠󸀠 (z) ; z, ζ) ≺≺ h (z) , (8) The univalent function q(z) is called a dominant of the solution of the strong differential subordination, or more a dominant, if p(z) ≺ q(z) for all p(z) satisfying (8).

Results

Conclusion