Classes of harmonic functions de ned by Salegean-type q-differential operators

Abstract

We consider complex-valued harmonic functions that are univalent and can be written in the form f = h + ḡ; where h and g are analytic, in a simply connected domain U and sense preserving in U, is that |h’(z)| > |g’(z)| in U: Making use of Salegean q-differential operators, we define a new subclasses harmonic starlike functions and obtain sufficient coefficient bounds, distortion theorems, and extreme points for f in the new function class. Moreover, we showed that these necessary coefficient bounds are also sufficient for those functions that have negative coeffcients.