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Fixed Point Theorems in Fuzzy B-Metric Spaces

M. Sohail Ashraf, Rashid Ali

Abstract


The study of fuzzy metric spaces was initiated by Kramosil and Michlek (1975) and later generalized by George and Veeramani (1994). Recently, Nădbăn (2016) investigated properties of fuzzy b-metric spaces and introduced the notion of fuzzy quasi-pseudo metric space. Grabeic (1988) extended well-known metric fixed point theorem in the setting of fuzzy metric spaces. The aim of this article is to study some fixed point theorems for self-mappings defined on fuzzy b-metric spaces which will be the continuation of the work of Nădbăn (2016). We proved the famous Banach contraction principle in the setting of a fuzzy b-metric space and hence generalized in this way the theorems proved by Grabeic. The theorem is illustrated by an example. We also established another fixed point result for certain self-mappings on fuzzy b-metric spaces. Our results generalize many pre-existing results in the literature. 


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