On the \(L\)-fuzzy Brouwer fixed point theorem
type: Item
instance of: scholarly article
title: On the \(L\)-fuzzy Brouwer fixed point theorem
zbMATH Open document ID: 0932.54011
DOI: 10.1016/S0165-0114(98)00327-3
author: Tomasz Kubiak
author: Dexue Zhang
published in: Fuzzy Sets and Systems
publication date: 2000-03-14T00:00:00Z
review text: Let \(L\) be a fuzzy lattice, i.e. a completely distributive lattice with an order-reversing involution. In the paper, the authors prove successfully that (1) the \(L\)-cube has the fixed point property (under the Hutton product \(L\)-topology); (2) the stratified \(L\)-cube is formed by the product of \(I^*(L)\) which is the stratification of the \(L\)-fuzzy interval \(I(L)\) [\textit{B. Hutton}, J. Math. Anal. Appl. 50, 74-79 (1975; Zbl 0297.54003)]. The stratified \(L\)-cubes have also the fixed point property when \(L\) has a countable base. The result (1) is a generalization of one obtained by \textit{T. Kubiak} [ibid. 223, No. 1, 62-66 (1998; Zbl 0907.54006)], under a rather strong assumption.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 1339627
zbMATH Keywords: stratified space
zbMATH Keywords: \(L\)-cube
zbMATH Keywords: \(L\)-fuzzy interval
reviewed by: Yingming Liu
MaRDI profile type: Publication
cites work: Q4693062
cites work: Q3941926
cites work: Q3898534
cites work: Q5509701
cites work: Normality in fuzzy topological spaces
cites work: Uniformities on fuzzy topological spaces
cites work: Separation axioms in fuzzy topological spaces
cites work: Q3965241
cites work: Q4010283
cites work: On \(L\)-Tychonoff spaces
cites work: The fuzzy Brouwer fixed-point theorem
cites work: Q3667583
cites work: Topological Lattices
cites work: Q4383385
cites work: Q4845811
Recommended article: The fuzzy Brouwer fixed-point theorem
Recommended article: Q5018938
Recommended article: On fixed point theorems for fuzzy mappings
Recommended article: Q3601701
Recommended article: Q4317115
Recommended article: Fixed point theorems for L-fuzzy mappings in quasi-pseudo metric spaces
Recommended article: Fixed points of \(\mathcal{L}\)-fuzzy mappings in ordered \(b\)-metric spaces
Recommended article: On the Brouwer fixed point theorem
Recommended article: Browder's fixed point theorem and some interesting results in intuitionistic fuzzy normed spaces
Recommended article: Q5741981
description: scientific article; zbMATH DE number 1339627