A first-order differential double subordination with applications

doi:10.1016/j.aml.2011.08.025

Applied Mathematics Letters

Volume 25, Issue 3, March 2012, Pages 268-274

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Abstract

Let $q_{1}$ and $q_{2}$ belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions $p$ to satisfy the double subordination chain $q_{1} (z) ≺ p (z) ≺ q_{2} (z)$ . The differential sandwich-type result obtained is applied to normalized univalent functions and to $Φ$ -like functions.

Keywords

Differential subordination

Differential superordination

Best subordinant

Best dominant

Φ

-like functions

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^☆: The works by the first and the fourth authors were supported in part by grants from the Universiti Sains Malaysia and the University of Delhi respectively. The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-0017111). This work was completed during the visit of the first and the fourth authors to Pukyong National University. The authors are thankful to the referees for their suggestions that helped improve the presentation of this manuscript.

Applied Mathematics Letters

A first-order differential double subordination with applications☆

Abstract

Keywords