Abstract
By using the concept of a class of functions, the $\mathcal {R}$ -functions, we provide some fuzzy fixed point theorems on a space of fuzzy sets equipped with the supremum metric. By presenting a technique of constructing a sequence of successive approximations, we obtain some interesting results that improve many existing results. The related cases are also shown and discussed.
Highlights
By using a natural generalization of the concept of a set, the fuzzy set, which was introduced initially by Zadeh [ ], considering mathematical programming problems which are expressed as optimizing some goal function given certain constraints, this be relaxed by means of a subjective gradation
In, Heilpern [ ] used the concept of fuzzy sets and introduced a class of fuzzy mappings, which is a generalization of the set-valued mapping, and proved a fixed point theorem for fuzzy contraction mappings in metric linear spaces
Several other authors have studied the existence of fixed points of fuzzy mappings; for example, Estruch and Vidal [ ] proved a fixed point theorem for fuzzy contraction mappings over a complete metric space, which is a generalization of the given Heilpern fixed point theorem, and Sedghi et al [ ] gave an extended version of the Estruch and Vidal [ ] theorem
Summary
By using a natural generalization of the concept of a set, the fuzzy set, which was introduced initially by Zadeh [ ], considering mathematical programming problems which are expressed as optimizing some goal function given certain constraints, this be relaxed by means of a subjective gradation. They proved the following common fixed point theorem for a family of fuzzy mappings.
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