The aim of the present paper is to study a certain subclass of harmonic univalent functions with varying arguments defined by Salegean operator. For this class we determine a sufficient coefficient condition, representation theorem, distortion theorem, extreme points. Mathematics Subject Classification: Primary 30C45; Secondary 30C80

Ruscheweyh and Sheil-Small proved that convexity is preserved under the convolution of univalent analytic mappings in K. However, when we consider the convolution of univalent harmonic convex mappings in K H , this property does not hold. In fact, such convolutions may not be univalent. We establish some results concerning the convolution of univalent harmonic convex mappings provided that it i...

A recent result of Sibel Yalcin et al. [4] appeared in “Journal of Inequalities in Pure and Applied Mathematics”(2007) concerning the convolution of two harmonic univalent functions in the class RSH (k, γ) is improved. 2010 Mathematics Subject Classification: 30C45.

Making use of Srivastava-Wright operator we introduced a new class of complexvalued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, extreme points, distortion bounds, convex combination. Mathematics subject classification (2010): 30C45.

The purpose of the present paper is to establish some results involving coefficient conditions, distortion bounds, extreme points, convolution, convex combinations and neighborhoods for a new class of harmonic univalent functions in the open unit disc. We also discuss a class preserving integral operator. Relevant connections of the results presented here with various known results are briefly ...

Let H be the class of complex-valued harmonic mappings f=h+g¯ defined in unit disk D:={z?C:|z|<1}, where h and g are analytic functions D with normalization h(0)=0=h?(0)?1 g(0)=0. H0={f=h+g¯?H:g?(0)=0}. PH0(M):={f=h+g¯?H0:Re(zh??(z))>?M+|zg??(z)|,z?DandM>0}. univalent [Ghosh N, Allu V. On some subclasses mappings. Bull Aust Math Soc. 2020;101:130–140.]. In this paper, we obtain sharp Bohr–Rogos...

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...