Title of article :
On Some Properties of Log-Harmonic Functions Product
Author/Authors :
Alizadeh, Mehri Department of Mathematics - Faculty of Science - PNU University, Tehran, Iran , Aghalary, Rasoul Department of Mathematics - Faculty of Science - Urmia University, Urmia, Iran , Ebadian, Ali Department of Mathematics - Faculty of Science - Urmia University, Urmia, Iran
Abstract :
In this paper we define a new subclass SLH(k, γ; φ)
of log-harmonic mappings, and then basic properties such as dila-
tions, convexity on one direction and convexity of log functions of
convex- exponent product of elements of that class are discussed.
Also we find sufficient conditions on β such that f ∈ SLH(k, γ; φ)
leads to F(z) = f(z)|f(z)|
2β ∈ SLH(k, γ, φ). Our results generalize
the analogues of the earlier works in the combinations of harmonic
functions.
Keywords :
Univalent function , Log-harmonic function , Convex in the one direction , Sense-preserving functions
Journal title :
Sahand Communications in Mathematical Analysis
