Norm of the pre-Schwarzian derivative, Bloch's constant and coefficient bounds in some classes of harmonic mappings

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:474

Article

Kanas, S.¹  Maharana, S.²  Prajapat, J. K.² 

[1] Univ Rzeszow, Fac Math & Nat Sci, Ul S Pigonia 1, PL-35310 Rzeszow, Poland

[2] Cent Univ Rajasthan, Dept Math, Kishangarh 305817, Rajasthan, India

关键词: Harmonic mapping;    Functions convex in one direction;    Schwarzian derivative;    Pre-Schwarzian derivative;    Univalent harmonic mapping;    Bloch constant;   

DOI  :  10.1016/j.jmaa.2019.01.080

来源: Elsevier

【 摘 要 】

The aim of the paper is a study of a family of sense-preserving complex valued harmonic functions f that are normalized in the open unit disk, and such that its analytic part is convex in one direction. We prove the univalence and establish estimates on pre-Schwarzian derivative and the Bloch constant for co-analytic part of harmonic mapping. The bounds of the coefficients of co-analytic part are also given. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free