Recommended by Narendra Kumar Govil We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions their boundaries are determined explicitly and the proofs rely on Schw...

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

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...

The first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right halfplane mapping or a normalized vertical strip mapping is convex in the direction of the real axis. provided that it is locally univalent. In this paper, we prove that in general the assumption of local univalency cannot be omitted. However, we are able to show t...

Quantitative estimates are obtained for the (finite) valence of functions analytic in the unit disk with Schwarzian derivative that is bounded or of slow growth. A harmonic mapping is shown to be uniformly locally univalent with respect to the hyperbolic metric if and only if it has finite Schwarzian norm, thus generalizing a result of B. Schwarz for analytic functions. A numerical bound is obt...

Abstract In this paper we introduce a new family Ā(α, β, γ) of harmonic univalent functions with negative coefficients using fractional calculus operator Ωλwhich contains various well known classes of harmonic univalent functions as well as many new ones. We obtain coefficient estimate, distortion theorem and various other properties for functions belonging to the class Ā(α, β, γ) in the unit d...