ON A CERTAIN SUBClASSES OF ANALYTIC FUNCTIONS INVOLVING DIFFERENTIAL OPERATOR

Suhila Elhaddad, Maslina Darus
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia
Huda Aldweby
Department of Mathematics, Faculty of Science, AL Asmaraya Islamic University, Libya

Abstract 

In this paper, a new subclass in the open unit disc of analytic functions is introduced. This subclass TS m,α λ,β (ζ, ϑ) is mainly defined by a specific differential operator. A coefficient inequality is obtained and other properties like distortion and closure theorems are derived. Moreover, extreme points of differential operator are also given. Additionally, Hadamard products (or convolution) of functions respective to the class are also included. 

2010 Mathematics Subject Classification. 30C45, 30C50. 

Keywords and phrases. Analytic function, Mittag-Leffler function, differential operator, Hadamard product.

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