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.

In this paper, we prove some fixed points, coupled coincidence point and coupled common fixed point results for mappings satisfying an almost generalized contraction conditions in partially ordered [Formula: see text]-metric spaces. These results generalize, extend and unify many comparable results in the existing literature. Few examples are given to support our results.

The purpose of this paper is to establish some xed point results for a class of generalized (φ, ψ)-weak contraction mapping in complete partially ordered b-metric space. This mapping necessarily have a unique xed point under ordered relation in the space. Also, the results for common xed point and coincidence point of the self mappings are presented. These results generalize and extend an existing results in the literature. Some illustrations are given at the end to support the results.

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