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 ...

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...

Let HC ( ? ) and c denote the classes of sense-preserving harmonic mappings f = h + g ¯ in D with dilation ? z ? for | < 1 such that is Ma–Minda type convex function respect to conjugate points respectively. Here, : ? ? , called function, analytic univalent has positive real part, symmetric axis, starlike 0 > . The are derived from work Sun et al. (2016) on class M ? We study growth theorems fu...

The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, ∆, such that f = h + g where h(z) = z + ∑∞ 2 akz , g(z) = ∑∞ 1 bkz . Using a technique from Clunie and Sheil-Small, we construct a family of 1-slit mappings in SH by varying ω(z) = g ′(z)/f ′(z). As ω(z) changes, the tip of the slit slides along the negative real axis from the point 0 to −1. In doin...

The main aim of this paper is to introduce three classes $H^0_{p,q}$, $H^1_{p,q}$ and $TH^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. First, we discuss the starlikeness and convexity of mappings in $H^0_{p,q}$ and $H^1_{p,q}$. Then establish the covering theorem for mappings in $H^1_{p,q}$. Finally, we determine the extreme points of the class $TH^*_{p}$.

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 short note we apply certain iteration of the Janowski functions to estimate the integral means of some analytic and univalent mappings of |z| < 1. Our method of proof follows an earlier one due to Leung [4].

Let H0 denote the set of all sense-preserving harmonic mappings f=h+g‾ in unit disk D, normalized with h(0)=g(0)=g′(0)=0 and h′(0)=1. In this paper, we mainly investigate some properties certain subclasses H0, including inclusion relations stability analysis by precise examples, coefficient bounds, growth, covering distortion theorems. As applications, build Bohr inequalities for these means su...