Some fixed point results of generalized [Formula: see text] -contractive mappings in ordered b-metric spaces

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 [Formula: see text] -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 [Formula: see text] -contractive conditions in complete partially ordered b-metric spaces are proved. These results generalize several comparable results in the existing literature.