The purpose of the present paper is to study a certain subclass of harmonic univalent functions associated with Dziok-Srivastava operator. We obtain coefficient conditions, distortion bounds, and extreme points for the above class of harmonic univalent functions belonging to this class and discuss a class preserving integral operator. We also show that class studied in this paper is closed unde...

‎In this paper,  the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.

We consider the class of univalent log-harmonic mappings on unit disk. Firstly, we present general idea constructing Koebe mappings, right half-plane and two-slits then show precise ranges these mappings. Moreover, coefficient estimates for starlike are obtained. Growth distortion theorems certain special subclasses studied. Finally, propose two conjectures, namely, covering conjectures.

A continuous function f = u + iv is a complex valued harmonic function in a complex domain C if both u and v are real harmonic in C. In any simply connected domain D ⊂ C we can write f(z) = h + g, where h and g are analytic in D. We call h the analytic part and g the co-analytic part of f . A necessary and sufficient condition for f to be locally univalent and sense-preserving in D is that |h′(...

A continuous function f u iv is a complex-valued harmonic function in a complex domain Ω if both u and v are real and harmonic inΩ. In any simply connected domainD ⊂ Ω, we can write f h g, where h and g are analytic inD. We call h the analytic part and g the coanalytic part of f . A necessary and sufficient condition for f to be locally univalent and orientation preserving in D is that |h′ z | ...

The purpose of the present paper is to establish connections between various subclasses of harmonic functions by applying certain convolution operator involving hypergeometric functions. To be more precise, we investigate such connections with Goodman-Rønning-type harmonic univalent functions in the open unit disc U .

Though connections between a well established theory of analytic univalent functions and hypergeometric functions have been investigated by several researchers, yet analogous connections between planer harmonic mappings and hypergeometric functions have not been explored. The purpose of this paper is to uncover some of the inequalities associating hypergeometric functions with planer harmonic m...