%0 Journal Article
%T Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator
%A K. Vijaya
%A G. Murugusundaramoorthy
%A M. Kasthuri
%J International Journal of Analysis
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/793709
%X Making use of a Salagean operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. Among the results presented in this paper including the coeffcient bounds, distortion inequality, and covering property, extreme points, certain inclusion results, convolution properties, and partial sums for this generalized class of functions are discussed. 1. Introduction and Preliminaries A continuous function is a complex-valued harmonic function in a complex domain if both and are real and harmonic in . In any simply connected domain , we can write , where and are analytic in . We call the analytic part and the coanalytic part of . A necessary and sufficient condition for to be locally univalent and orientation preserving in is that in (see [1]). Denote by the family of functions which are harmonic, univalent, and orientation preserving in the open unit disc so that is normalized by . Thus, for , the functions and are analytic in and can be expressed in the following forms: and is then given by We note that the family of orientation preserving, normalized harmonic univalent functions reduces to the well-known class of normalized univalent functions if the coanalytic part of is identically zero; that is, . For functions , Jahangiri et al. [2] defined Salagean operator on harmonic functions given by where In 1975, Silverman [3] introduced a new class of analytic functions of the form and opened up a new direction of studies in the theory of univalent functions as well as in harmonic functions with negative coefficients [4]. Uralegaddi et al. [5] introduced analogous subclasses of star-like, convex functions with positive coefficients and opened up a new and interesting direction of research. In fact, they considered the functions where the coefficients are positive rather than negative real numbers. Motivated by the initial work of Uralegaddi et al. [5], many researchers (see [6¨C9]) introduced and studied various new subclasses of analytic functions with positive coefficients but analogues results on harmonic univalent functions have not been explored in the literature. Very recently, Dixit and Porwal [10] attempted to fill this gap by introducing a new subclass of harmonic univalent functions with positive coefficients. Denote by the subfamily of consisting of harmonic functions of the form Motivated by the earlier works of [11¨C14] on the subject of harmonic functions, in this paper an attempt has been made to study the class of functions associated with Salagean operator on harmonic
%U http://www.hindawi.com/journals/ijanal/2014/793709/