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

Abstract

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.

Keywords

• differential operator
• gamma function
• Hadamard product
• Hurwitz-Lerch zeta function
• meromorphic functions
• q-hypergeometric function
• subordination property