Harmonic Close-to-Convex Mappings Associated with Salagean q-differential Operator

Abstract

In this paper, we define a new subclass (Formula presented) of analytic functions and a new subclass (Formula presented) of harmonic functions (Formula presented) associated with Sălăgean q-differential operator. We prove that a harmonic function (Formula presented) belongs to the class (Formula presented) if and only if the analytic functions h+∊g belong to (Formula presented) for each ∊ (|∊| = 1), and using a method by Clunie and Sheil-Small, we determine a sufficient condition for the class (Formula presented) to be close-to-convex. We provide sharp coefficient estimates, sufficient coefficient condition, and convolution properties for such functions classes. We also determine several conditions of partial sums of (Formula presented).