Existence Theorems for Generalized Distance on Complete Metric Spaces

Existence Theorems for Generalized Distance on Complete Metric Spaces

We first introduce the new concept of a distance called u-distance, which generalizes w-distance, Tataru's distance, and τ-distance. Then we prove a new minimization theorem and a new fixed point theorem by using a u-distance on a complete metric space. Our results extend and unif...

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Main Author: Jeong Sheok Ume
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Fixed Point Theory and Applications
Online Access:http://dx.doi.org/10.1155/2010/397150
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spelling doaj-524be9098a8942518271b405dd11afc12020-11-25T00:38:52ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-01201010.1155/2010/397150Existence Theorems for Generalized Distance on Complete Metric SpacesJeong Sheok UmeWe first introduce the new concept of a distance called u-distance, which generalizes w-distance, Tataru's distance, and τ-distance. Then we prove a new minimization theorem and a new fixed point theorem by using a u-distance on a complete metric space. Our results extend and unify many known results due to Caristi, Ćirić, Ekeland, Kada-Suzuki-Takahashi, Kannan, Ume, and others. http://dx.doi.org/10.1155/2010/397150
collection DOAJ
language English
format Article
sources DOAJ
author Jeong Sheok Ume
spellingShingle Jeong Sheok Ume
Existence Theorems for Generalized Distance on Complete Metric Spaces
Fixed Point Theory and Applications
author_facet Jeong Sheok Ume
author_sort Jeong Sheok Ume
title Existence Theorems for Generalized Distance on Complete Metric Spaces
title_short Existence Theorems for Generalized Distance on Complete Metric Spaces
title_full Existence Theorems for Generalized Distance on Complete Metric Spaces
title_fullStr Existence Theorems for Generalized Distance on Complete Metric Spaces
title_full_unstemmed Existence Theorems for Generalized Distance on Complete Metric Spaces
title_sort existence theorems for generalized distance on complete metric spaces
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2010-01-01
description We first introduce the new concept of a distance called u-distance, which generalizes w-distance, Tataru's distance, and τ-distance. Then we prove a new minimization theorem and a new fixed point theorem by using a u-distance on a complete metric space. Our results extend and unify many known results due to Caristi, Ćirić, Ekeland, Kada-Suzuki-Takahashi, Kannan, Ume, and others.
url http://dx.doi.org/10.1155/2010/397150
work_keys_str_mv AT jeongsheokume existencetheoremsforgeneralizeddistanceoncompletemetricspaces
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