Document Type : Research Paper

Author

• Gholamreza Heidary Joonaghany

Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran

Abstract

In this paper, by providing an example, we show that the condition which produced by Radenovi'{c} and Kadelburg in [Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010) pp. 1776-1783] is not sufficient for the uniqueness of the fixed point. Furthermore, a new sufficient condition is introduced for the uniqueness of the fixed point. Some suitable examples are furnished to demonstrate the validity of the hypotheses of our results.

Keywords

• Fixed point
• Generalized $(\psi
• \phi)$-Weak Contraction
• Ordered metric space