Abstract -A complex-valued functions that are univalent and sense preserving in the unit disk U can be written in the form ( ) ( ) ( ) f z h z g z   , where U(z) and g(z) are analytic in. We will introduced the operator D which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(,, n) by generalized derivative operator of harmonic un...

In this paper, we investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points and convex combination of a new subclass of harmonic univalent functions defined by a generalization of modified Salagean operator. 2000 Mathematics Subject Classification: 30C45, 30C50. 1.Introduction Let H denote the family of continuous complex valued harmonic functions which are ...

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 continuous function f u iv is a complex-valued harmonic function in a simply connected complex domain D ⊂ C if both u and v are real harmonic in D. It was shown by Clunie and Sheil-Small 1 that such harmonic function can be represented by f h g, where h and g are analytic in D. Also, a necessary and sufficient condition for f to be locally univalent and sense preserving in D is that |h′ z | >...

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...

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 .

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...