Differential inequalities imposed by the extended hypergeometric function

Rabha W Ibrahim; M Z Ahmad; Hiba F Al-Janaby

doi:10.1186/s40064-016-1996-9

Differential inequalities imposed by the extended hypergeometric function

Springerplus. 2016 Mar 25:5:375. doi: 10.1186/s40064-016-1996-9. eCollection 2016.

Authors

Rabha W Ibrahim¹, M Z Ahmad², Hiba F Al-Janaby²

Affiliations

¹ Faculty of Computer Science and Information Technology, University Malaya, 50603 Kuala Lumpur, Malaysia.
² Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Malaysia.

Abstract

Recently, the generalized hypergeometric function is extended by utilizing the Beta function. Based on this type of function, we introduce a new operator in the open unit disk. The present article investigates some subordination and superordination results for certain normalized analytic functions in the open unit disk, which are acted upon by the generalized Noor integral operator. Some of outcomes improve and generalize previously known outcomes.

Keywords: Analytic function; Hypergeometric function; Integral operator; Subordination; Superordination; Unit disk; Univalent function.