Existence theorems for generalized distance on complete metric spaces
type: Item
instance of: scholarly article
title: Existence theorems for generalized distance on complete metric spaces
zbMATH Open document ID: 1203.54050
DOI: 10.1155/2010/397150
published in: Fixed Point Theory and Applications
publication date: 2010-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/228370
review text: First, the author introduces the concept of \(u\)-distance on a metric space, as a generalization of the \(w\)-distance (concept due to \textit{O. Kada, T. Suzuki} and \textit{W. Takahashi} [Math. Jap. 44, No.~2, 381--391 (1996; Zbl 0897.54029)]). Then he obtains a generalization of Takahashi's minimization theorem based on which several existence theorems are established for problems of the following type:\ Given a complete metric pace \((X,d)\), a \(u\)-distance \(p\) on \(X\) and a self-mapping \(T\) of \(X\), find \(x_0\in X\) such that \(Tx_0=x_0\) and \(p(x_0, x_0)=0\).
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 5792443
zbMATH Keywords: complete metric space
zbMATH Keywords: \(u\)-distance
zbMATH Keywords: minimization theorem
zbMATH Keywords: fixed point
Wikidata QID: Q59253810
author: Jeong Sheok Ume
MaRDI profile type: Publication
OpenAlex ID: W1997792631
cites work: Nonconvex minimization problems
cites work: Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
cites work: Q4359066
cites work: Generalized distance and existence theorems in complete metric spaces
cites work: Q4308660
cites work: Contractive mappings, Kannan mappings and metric completeness
cites work: Q4345456
cites work: Fixed point theorems and characterizations of metric completeness
cites work: Fixed point theorems related to Ćirić's contraction principle
cites work: Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms
cites work: A Generalization of Banach's Contraction Principle
cites work: Some Results on Fixed Points--II
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description: scientific article; zbMATH DE number 5792443