Abstract
In this paper, some common fixed point theorems for Lipschitz-type fuzzy mappings in complete metric spaces are obtained. As applications, we establish some common fixed point theorems for Lipschitz-type multi-valued mappings in complete metric spaces. Also, we give an example to show the validity of our results, which indicates that our results improve and extend several known results in the existing literature.MSC:47H10, 47H04, 26A16.
Highlights
Introduction and preliminariesThe study of fixed point theorems in fuzzy mathematics was instigated by Weiss [ ] and Butnariu [ ]
The aim of this paper is to investigate some common fixed point theorems for Lipschitztype fuzzy mappings in complete metric spaces
We establish some common fixed point theorems for Lipschitz-type multi-valued mappings in complete metric spaces
Summary
Introduction and preliminariesThe study of fixed point theorems in fuzzy mathematics was instigated by Weiss [ ] and Butnariu [ ]. Main results we will establish some common fixed point theorems for a pair of Lipschitztype fuzzy mappings in complete metric spaces. Let (X, d) be a complete metric space, and let S, T : X → F (X) be two Lipschitz-type fuzzy mappings satisfying the following conditions: (a) for each x ∈ X, there exists α(x) ∈ ( , ] such that [Sx]α(x), [Tx]α(x) are nonempty closed bounded subsets of X, and (b) for all x, y ∈ X, H [Sx]α(x), [Ty]α(y)
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