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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo

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Volume 13, Issue 1


Volume 13 (2015)

Inequalities of harmonic univalent functions with connections of hypergeometric functions

Janusz Sokół
  • Department of Mathematics, Rzeszów University of Technology, Al. Powsta´nców Warszawy 12, 35-959 Rzeszów, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Rabha W. Ibrahim
  • Faculty of Computer Science and Information Technology, University Malaya, 50603 Kuala Lumpur, Malaysia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ M. Z. Ahmad / Hiba F. Al-Janaby
Published Online: 2015-10-21 | DOI: https://doi.org/10.1515/math-2015-0066


Let SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in the open unit disk U = { z : |z| < 1} for which f (0) = f'(0)-1=0. In this paper, we introduce and study a subclass H( α, β) of the class SH and the subclass NH( α, β) with negative coefficients. We obtain basic results involving sufficient coefficient conditions for a function in the subclass H( α, β) and we show that these conditions are also necessary for negative coefficients, distortion bounds, extreme points, convolution and convex combinations. In this paper an attempt has also been made to discuss some results that uncover some of the connections of hypergeometric functions with a subclass of harmonic univalent functions.

Keywords: Harmonic function; Analytic function; Univalent function; Unit disk


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About the article

Received: 2015-04-01

Accepted: 2015-09-16

Published Online: 2015-10-21

Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0066.

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©2015 Sokół et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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