Sufficient coefficient conditions for complex functions to be close-to-convex harmonic or convex harmonic are given. Construction of close-to-convex harmonic functions is also studied by looking at transforms of convex analytic functions. Finally, a convolution property for harmonic functions is discussed. Harmonic, Convex, Close-to-Convex, Univalent.

In this paper, we consider and investigate the relative harmonic preinvex functions, which unifies several new known classes of harmonic preinvex functions. We derive several new integral inequalities such as Hermite-Hadamard, Simpson’s, trapezoidal for the relative harmonic preinvex functions. Since the relative harmonic preinvex functions include, convex function, harmonic convex functions, p...

in the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.

Sato’s hyperfunctions are known to be represented as the boundary values of harmonic functions as well as those of holomorphic functions. The author obtains a bijective Poisson mapping P : S∗′(Rn) −→ S∗′(S∗Rn) ∩H(S∗Rn) where H(S∗Rn) is a kind of Hardy subspace of B(S∗Rn). Moreover, the author has an isomorphism between Sobolev spaces P : W (R) −→ W s+(n−1)/4(S∗Rn) ∩H(S∗Rn). There are some simil...

‎Complex-valued harmonic functions that are univalent and‎ ‎sense-preserving in the open unit disk $U$ can be written as form‎ ‎$f =h+bar{g}$‎, ‎where $h$ and $g$ are analytic in $U$‎. ‎In this paper‎, ‎we introduce the class $S_H^1(beta)$‎, ‎where $1<betaleq 2$‎, ‎and‎ ‎consisting of harmonic univalent function $f = h+bar{g}$‎, ‎where $h$ and $g$ are in the form‎ ‎$h(z) = z+sumlimits_{n=2}^inf...

A necessary and sufficient coefficient is given for functions in a class of complexvalued harmonic univalent functions using the Dziok-Srivastava operator. Distortion bounds, extreme points, an integral operator, and a neighborhood of such functions are considered.

Earlier versions of this software focused on algorithms arising from the material in the book Harmonic Function Theory [ABR] by Sheldon Axler, Paul Bourdon, and Wade Ramey. That book is still the source for many of the algorithms used in the HFT10.m package, but the goal of the package has expanded to include additional symbolic manipulations involving harmonic functions. The HFT10.m package ca...

We consider a class T O H of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class.