Close-to-starlike logharmonic mappings

Typically Real Logharmonic Mappings

The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form f z zh z g z defined on the open unit disc U. The functions are in the class of the generalized Janowski starlike log-harmonic mapping, Slh A,B, α , with the functional zh z in the class of the generalized Janowski starlike functions, S∗ A,B, α . By means ...

A Note on Logharmonic Mappings

where (a) m is nonnegative integer, (b) β= a(0)(1+a(0))/(1−|a(0)|2) and therefore, β >−1/2, (c) h and g are analytic in U , g(0)= 1, and h(0)≠ 0. Univalent logharmonic mappings on the unit disc have been studied extensively. For details see [1, 2, 3, 4, 5, 6, 7, 8]. Suppose that f is a univalent logharmonic mapping defined on the unit disc U . Then, if f(0) = 0, the function F(ζ) = log(f (eζ)) ...

A Factorization Theorem for Logharmonic Mappings

We give the necessary and sufficient condition on sense-preserving logharmonic mapping in order to be factorized as the composition of analytic function followed by a univalent logharmonic mapping. Let D be a domain of C and denote by H(D) the linear space of all analytic functions defined on D. A logharmonic mapping is a solution of the nonlinear elliptic partial differential equation f z = a ...

Harmonic Close-to-convex Mappings

Sufficient coefficient conditions for complex functions to be close-to-convex harmonic or convex harmonic are given. Construction of close-to-convex harmonic functions is also studied by looking at transforms of convex analytic functions. Finally, a convolution property for harmonic functions is discussed. Harmonic, Convex, Close-to-Convex, Univalent.