Some fixed point theorem using non- expansive mapping in b-metric space

Abstract

In this paper, we establish fixed point results for a class of nonexpansive self-mappings defined on complete b-metric spaces. Motivated by the work of Mohammadi, Golkarmanesh, and Parvaneh[7], the present study extends and generalizes existing fixed point results for nonexpansive mappings under suitable contractive conditions. The main results are obtained for mappings defined on a b-metric space endowed with a binary relation satisfying an appropriate invariance condition. By constructing a Picard sequence from a suitable initial point, we prove that the resulting sequence is Cauchy and converges to a fixed point in the complete b-metric space. Furthermore, the results provide conditions concerning the existence and separation of fixed points. The proposed results extend earlier findings and contribute to the development of fixed point theory by incorporating the generalized structure of b-metric spaces and weaker contractive conditions. These results may be useful in the study of nonlinear analysis and mathematical models in which the standard metric space framework is insufficient[6,5].