Fixed point results of $(\phi,\psi)$-weak contractions in ordered $b$-metric spaces

Abstract

The purpose of this paper is to prove some results on fixed point, coincidence point, coupled coincidence point and coupled common fixed point for the mappings satisfying generalized $(\phi, \psi)$-contraction conditions in complete partially ordered $b$-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. A few examples are illustrated to support our findings.

Keywords

• fixed point
• coupled coincidence point
• coupled common fixed point
• partially ordered b-metric space
• compatible
• mixed f-monotone