Common fixed points of fuzzy mappings
type: Item
instance of: scholarly article
title: Common fixed points of fuzzy mappings
zbMATH Open document ID: 0797.54022
DOI: 10.1016/0165-0114(93)90203-T
author: Jong Yeoul Park
author: Jae Ug Jeong
published in: Fuzzy Sets and Systems
publication date: 1994-10-19T00:00:00Z
review text: Let \((X,d)\) be a complete metric linear space and \(T_ 1\), \(T_ 2\) be fuzzy mappings from \(X\) into the set \(W(X)\) of the approximate quantities of \(X\) such that \(D(T_ 1x_ n,T_ 2x) \to 0\) for any sequence \(\{x_ n\}\) of \(X\) converging to \(x\). Main theorem: if there exist non-negative real numbers \(\alpha_ i,\alpha_ 1 + \alpha_ 2 + \alpha_ 4 + \alpha_ 5 \leq 1\), such that for all \(x\), \(y\) in \(X\), \[ \begin{aligned} [D(T_ 1 x,T_ 2y)]^ 2 & \leq \alpha_ 1 \cdot [d(x,y)]^ 2 + \alpha_ 2 \cdot p(x,T_ 1 x) \cdot p(y,T_ 2 y)\;+\\ & + \alpha_ 3 \cdot p(x,T_ 2 y)\cdot p(y,T_ 1 x) + \alpha_ 4 \cdot d(x,y) \cdot p(x,T_ 1 x) + \alpha_ 5 \cdot d(x,y) \cdot p(y,T_ 2 y)\end{aligned} \] then \(\{z\} \subseteq T_ 1(z) \cap T_ 2(z)\) for some point \(z\) in \(X\). Here \(D\) and \(p\) are suitable distances defined on the fuzzy sets of \(X\). Two other related results are given for \(S\)-convex structures on \(X\).
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 516638
zbMATH Keywords: complete metric linear space
zbMATH Keywords: \(S\)-convex structures
reviewed by: Salvatore Sessa
MaRDI profile type: Publication
cites work: Fuzzy mappings and fixed point theorems
cites work: Fuzzy mappings and fixed point theorem
cites work: Some fixed point theorems for fuzzy mappings
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description: scientific article; zbMATH DE number 516638