Abstract
Abstract We prove the existence of common fuzzy fixed points for a sequence of locally contractive fuzzy mappings satisfying generalized Banach type contraction conditions in a complete metric space by using iterations. Our main result generalizes and unifies several well-known fixed-point theorems for multivalued maps. Illustrative examples are also given. MSC:46S40, 47H10, 54H25.
Highlights
1 Introduction The Banach contraction theorem and its subsequent generalizations play a fundamental role in the field of fixed point theory
Heilpern introduced in [ ] the notion of a fuzzy mapping in a metric linear space and proved a Banach type contraction theorem in this framework
The aim of this paper is to prove a common fixed-point theorem for a sequence of fuzzy mappings in the context of metric spaces without the assumption of linearity
Summary
The Banach contraction theorem and its subsequent generalizations play a fundamental role in the field of fixed point theory. Below) we establish a common fixed-point theorem for a sequence of generalized fuzzy uniformly locally contraction mappings on a complete metric space without the requirement of linearity.
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