Abstract
ObjectivesThe 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 )-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.ResultThe 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 )-contractive conditions in complete partially ordered b-metric spaces are proved. These results generalize several comparable results in the existing literature.
Highlights
Introduction and preliminariesIn analysis, the Banach contraction principle is one of the most important results and plays a crucial role in various fields of applied mathematics and scientific applications
While the concept of coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings having monotone property in partially ordered complete metric spaces was first initiated by Lakshmikantham and Ćirić [20]
In this article some fixed point, coincidence, coupled coincidence and coupled common fixed points theorems are proved for mappings satisfying generalized (φ, ψ) -contractions in complete partially ordered b-metric spaces
Summary
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 (φ, ψ)-contractive conditions in complete partially ordered b-metric spaces are proved. These results generalize several comparable results in the existing literature. While the concept of coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings having monotone property in partially ordered complete metric spaces was first initiated by Lakshmikantham and Ćirić [20]. In this article some fixed point, coincidence, coupled coincidence and coupled common fixed points theorems are proved for mappings satisfying generalized (φ, ψ) -contractions in complete partially ordered b-metric spaces.
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