Publication: q-Harmonic mappings for which analytic part is q-convex functions of complex order
Date
2018
Authors
Çetinkaya, Asena
Polatoğlu, Yaşar
Journal Title
Journal ISSN
Volume Title
Publisher
Hacettepe Univ, Fac Sci, Hacettepe Univ, Fac Sci, Beytepe, Ankara 06800, Turkey
Abstract
We introduce a new class of harmonic function f, that is subclass of planar harmonic mapping associated with q-difference operator. Let h and g are analytic functions in the open unit disc D = {z : vertical bar z vertical bar < 1}. If f = h + <(g)over bar> is the solution of the non-linear partial differential equation w(q)(z) - D(q)g(z)/D(q)h(z) - (f) over bar(z) over bar /fz with vertical bar w(q)(z)vertical bar < 1, w(q)(z) (sic) b(1)1+z/1-qz and h is q-convex function of complex order, then the class of such functions are called q-harmonic functions for which analytic part is q-convex functions of complex order denoted by S-HCq(b). Obviously that the class S-HCq(b) is the subclass of S-H. In this paper, we investigate properties of the class S-HCq(b) by using subordination techniques.
Description
Keywords
q-difference operator, q-harmonic mapping, q-convex function of complex order