Abstract
The aim of this paper is to introduce generalized F2-Geraghty type fuzzy mappings on a metric space for establishing the existence of fuzzy fixed points of such mappings. As an application of our result, we obtain the existence of common fuzzy fixed point for a generalized F2-Geraghty type fuzzy hybrid pair. These results unify, generalize and complement various known comparable results in the literature. An example and an application to theoretical computer science are presented to support the theory proved herein. Also, to suggest further research on fuzzy mappings, a Feng–Liu type theorem is proved.
Highlights
Introduction and preliminariesBanach contraction principle [4] is constructive in nature and is one of the most useful tools in the study of nonlinear equations
The aim of this paper is to introduce generalized F2-Geraghty type fuzzy mappings on a metric space for establishing the existence of fuzzy fixed points of such mappings
Extensions of Geraghty result for multivalued mappings have been obtained in different directions [9, 10, 19], which in turn generalize a well-known Nadler’s fixed point theorem [15], a multivalued version of Banach contraction principle
Summary
Banach contraction principle [4] is constructive in nature and is one of the most useful tools in the study of nonlinear equations. Extensions of Geraghty result for multivalued mappings have been obtained in different directions [9, 10, 19], which in turn generalize a well-known Nadler’s fixed point theorem [15], a multivalued version of Banach contraction principle. Heilpern [12] initiated the concept of fuzzy mappings on a metric space and proved a fixed point theorem as a generalization of Nadler’s theorem [15]. Abu-Donia [1] studied the Hausdorff metric between fuzzy subsets via its correspondence between classical sets and obtained common fixed point theorems for fuzzy mappings, see [13]. We introduce generalized Geraghty type fuzzy mapping over a metric space (X, d).
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