Remarks on the Paper ``Coupled Fixed Point Theorems for Single-Valued Operators in b-Metric Spaces''

Abstract

In this paper, we improve some recent coupled fixed point results for single-valued operators in the framework of ordered b-metric spaces established by Bota et al. [M-F. Bota, A. Petrusel, G. Petrusel and B. Samet, Coupled fixed point theorems for single-valued operators in b-metric spaces, Fixed Point Theory Appl. (2015) 2015:231]. Also, we prove that Perov-type fixed point theorem in ordered generalized $b$-metric spaces is equivalent with Ran-Reurings-type theorem in ordered b-metric spaces.

Keywords

• vector-valued metric
• ordered b-metric space
• coupled fixed point
• integral equation
• well-posed fixed point problem