Abstract
Common fixed point results for mappings satisfying locally contractive conditions on a closed ball in an ordered complete dislocated metric space have been established. The notion of dominated mappings is applied to approximate the unique solution of nonlinear functional equations. Our results improve several well-known conventional results.
Highlights
Introduction and PreliminariesLet T : X → X be a mapping
Fixed points results of mappings satisfying certain contractive conditions on the entire domain have been at the centre of rigorous research activity, and it has a wide range of applications in different areas such as nonlinear and adaptive control systems, parameterize estimation problems, computing magnetostatic fields in a nonlinear medium, and convergence of recurrent networks
Azam et al [18] very recently exploited the idea of fixed points and proved a significant result concerning the existence of fixed points for fuzzy mappings on closed ball in a complete metric space
Summary
Many results appeared related to fixed point theorems in complete metric spaces endowed with a partial ordering. Ran and Reurings [6] proved an analogue of Banach’s fixed point theorem in metric space endowed with a partial order and gave applications to matrix equations In this way, they weakened the usual contractive condition. Arshad et al [17] proved a significant result concerning the existence of fixed points of a mapping satisfying contractive conditions on closed ball in a complete dislocated metric space. We have obtained fixed point theorems for contractive dominated selfmappings in an ordered complete dislocated metric space on a closed ball to generalize, extend, and improve a classical fixed point result in [22].
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