On a Certain Subclass of Meromorphic Functions Defined by a New Linear Differential Operator

Khalid Challab (School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 Selangor D. Ehsan)
Maslina Darus (School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 Selangor D. Ehsan)
Firas Ghanim (Department of Mathematics, College of Sciences, University of Sharjah, Sharjah,)

Journal of Mathematical and Fundamental Sciences
Vol. 49 No. 3 (2017)

In this article, a new linear differential operator I^k (L_s^a (a_l,b_m )f(z)) is defined by using the Hadamard product of the q-hypergeometric function and a function related to the Hurwitz-Lerch zeta function. By using this linear differential operator, a new subclass L_(s,a)^(k,*) (α_l,β_m;A,B,b) of meromorphic functions is defined. Some properties and characteristics of this subclass are considered. These include the coefficient inequalities, the growth and distortion properties and the radii of meromorphic starlikeness and meromorphic convexity. Finally, closure theorems and extreme points are introduced.