Displaying similar documents to “Univalent harmonic mappings convex in one direction.”

A subclass of harmonic functions with varying arguments defined by Dziok-Srivastava operator

G. Murugusundaramoorthy, Kaliappan Vijaya, Ravinder Krishna Raina (2009)

Archivum Mathematicum

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Making use of the Dziok-Srivastava operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

Polatoğlu, Yaşar (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 30C45, 30C55 One of the most important questions in the study of the classes of such functions is related to bounds on the modulus of functions (growth) or modulus of the derivative (distortion). The aim of this paper is to give the growth and distortion theorems for the close-to-convex harmonic functions in the open unit disc D.

Nonbasic harmonic maps onto convex wedges

Josephi Cima, Alberti Livingston (1993)

Colloquium Mathematicae

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We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation f z ¯ = a f z where a(z) is a nontrivial extreme point of the unit ball of H ∞ .