Some fixed point results of generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive mappings in ordered b-metric spaces

Abstract

Abstract Objectives The aim of this paper is to establish some fixed point, coincidence point and, coupled coincidence and coupled common fixed point results for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive mappings in partially ordered b-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. Few examples are illustrated to justify our results. Result The existence and uniqueness theorems for a fixed point and coincidence point, coupled coincidence point and coupled common fixed points for two mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive conditions in complete partially ordered b-metric spaces are proved. These results generalize several comparable results in the existing literature.

Keywords

• Partially ordered b-metric space
• Fixed point
• Coupled coincidence point
• Coupled common fixed point
• Compatible
• Mixed f-monotone