Differential Subordination and Superordination Results Associated with Mittag–Leffler Function

Adel A. Attiya,Mohamed K. Aouf,Mansour F. Yassen,Ekram E. Ali

doi:10.3390/math9030226

Abstract

In this paper, we derive a number of interesting results concerning subordination and superordination relations for certain analytic functions associated with an extension of the Mittag–Leffler function.

Highlights

Let λ and h be two analytic functions in U, suppose
≺ μ2 ( z ), where μ1 and μ2 are given univalent functions in U with μ1 (0) = 1 and μ2 (0) = 1, while Obradovic and Owa [9] obtained some results of subordinations associated f (z) δ with
We obtained a number of interesting results concerning subordination and superγ,k ordination relations for the operator Hα,β ( f )(z) of analytic functions associated with an extension of the Mittag–Leffler function in the open unit disk U

Summary

Introduction

Let λ and h be two analytic functions in U, suppose If λ and Φ(λ(z), zλ (z), z2 λ (z); z) are univalent functions in U and if λ satisfies the secondorder superordination h(z) ≺ Φ(λ(z), zλ (z), z2 λ (z); z), (3) Ali et al [7], used Bulboaca’s results [5] and obtained the sufficient conditions for normalized analytic functions f to satisfy z f 0 (z)

Results

Conclusion