A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series

Abstract

To date, many interesting subclasses of analytic functions involving symmetrical points and other well celebrated domains have been investigated and studied. The aim of our present investigation is to make use of certain Janowski functions and a Mathieu-type series to define a new subclass of analytic (or invariant) functions. Our defined function class is symmetric under rotation. Some useful results like Fekete-Szegö functional, a number of sufficient conditions, radius problems, and results related to partial sums are derived.

On a Set of Generalized Janowski-Type Starlike Functions Connected With Mathieu-Type Series and Opoola Differential Operator

“…Suppose m = 0, then set S m,α,β,µ τ,σ,r (A, B) = S r (A, B), where S r (A, B) is the set studied by Liu et al [12]. Geometric function theorists have studied several geometric properties of many subsets of analytic functions defined by devise number of operators, for instance see [7][8][9].…”