Open Access
2014 ONE PARAMETER FAMILY OF UNIVALENT BIHARMONIC MAPPINGS
Y. Abu Muhanna, S. V. Bharanedhar, S. Ponnusamy
Taiwanese J. Math. 18(4): 1151-1169 (2014). DOI: 10.11650/tjm.18.2014.4066

Abstract

In this paper, we provide sufficient conditions to construct sense-preserving and univalent biharmonic mappings that arises from analytic functions which are not necessarily univalent in the unit disk $|z|\lt 1$. Also we state and prove several theorems under different weaker hypothesis in each case, leading to an affirmative answer to the radius problem posed by Y. Abu Muhanna in 2008.

Citation

Download Citation

Y. Abu Muhanna. S. V. Bharanedhar. S. Ponnusamy. "ONE PARAMETER FAMILY OF UNIVALENT BIHARMONIC MAPPINGS." Taiwanese J. Math. 18 (4) 1151 - 1169, 2014. https://doi.org/10.11650/tjm.18.2014.4066

Information

Published: 2014
First available in Project Euclid: 10 July 2017

zbMATH: 1357.31002
MathSciNet: MR3245435
Digital Object Identifier: 10.11650/tjm.18.2014.4066

Subjects:
Primary: 31A05 , 31A30
Secondary: 30C45

Keywords: biharmonic , close-to-convex and starlike mappings , harmonic , radius of univalence , Univalent

Rights: Copyright © 2014 The Mathematical Society of the Republic of China

Vol.18 • No. 4 • 2014
Back to Top