Generalized metric spaces: A survey

Banach’s contraction mapping principle is remarkable in its simplicity, yet it is perhaps the most widely applied fixed point theorem in all of analysis with special applications to the theory of differential and integral equations. Because the underlined space of this theorem is a metric space, the...

Full description

Saved in:
Bibliographic Details
Published in:Journal of fixed point theory and applications 2015-09, Vol.17 (3), p.455-475
Main Author: Khamsi, M. A.
Format: Article
Language:English
Subjects:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c321t-6b8a84cfdc318ca97fd1e06255a6afe6204a353d55bf3ba2bff2e945e8547e273
cites cdi_FETCH-LOGICAL-c321t-6b8a84cfdc318ca97fd1e06255a6afe6204a353d55bf3ba2bff2e945e8547e273
container_end_page 475
container_issue 3
container_start_page 455
container_title Journal of fixed point theory and applications
container_volume 17
creator Khamsi, M. A.
description Banach’s contraction mapping principle is remarkable in its simplicity, yet it is perhaps the most widely applied fixed point theorem in all of analysis with special applications to the theory of differential and integral equations. Because the underlined space of this theorem is a metric space, the theory that developed following its publication is known as the metric fixed point theory. Over the last one hundred years, many people have tried to generalize the definition of a metric space. In this paper, we survey the most popular generalizations and we discuss the recent uptick in some generalizations and their impact in metric fixed point theory.
doi_str_mv 10.1007/s11784-015-0232-5
format article
fullrecord <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s11784_015_0232_5</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s11784_015_0232_5</sourcerecordid><originalsourceid>FETCH-LOGICAL-c321t-6b8a84cfdc318ca97fd1e06255a6afe6204a353d55bf3ba2bff2e945e8547e273</originalsourceid><addsrcrecordid>eNp9j01LAzEURYMoWKs_wN2A6-h7-a67UrQKhW7qOmQyLzKlnZakFeqvd8qIS1fvLt653MPYPcIjAtingmid4oCag5CC6ws2QmOQW6vM5V-W7prdlLIGMCDQjtjDnDrKYdN-U1Nt6ZDbWJV9iFSeq2lVjvmLTrfsKoVNobvfO2Yfry-r2RtfLOfvs-mCRynwwE3tglMxNVGii2FiU4MERmgdTEhkBKggtWy0rpOsg6hTEjRRmpxWloSVY4ZDb8y7UjIlv8_tNuSTR_BnSz9Y-t7Sny297hkxMKX_7T4p-_XumLt-5j_QD1GyVBs</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Generalized metric spaces: A survey</title><source>Springer Link</source><creator>Khamsi, M. A.</creator><creatorcontrib>Khamsi, M. A.</creatorcontrib><description>Banach’s contraction mapping principle is remarkable in its simplicity, yet it is perhaps the most widely applied fixed point theorem in all of analysis with special applications to the theory of differential and integral equations. Because the underlined space of this theorem is a metric space, the theory that developed following its publication is known as the metric fixed point theory. Over the last one hundred years, many people have tried to generalize the definition of a metric space. In this paper, we survey the most popular generalizations and we discuss the recent uptick in some generalizations and their impact in metric fixed point theory.</description><identifier>ISSN: 1661-7738</identifier><identifier>EISSN: 1661-7746</identifier><identifier>DOI: 10.1007/s11784-015-0232-5</identifier><language>eng</language><publisher>Basel: Springer Basel</publisher><subject>Analysis ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics</subject><ispartof>Journal of fixed point theory and applications, 2015-09, Vol.17 (3), p.455-475</ispartof><rights>Springer Basel 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c321t-6b8a84cfdc318ca97fd1e06255a6afe6204a353d55bf3ba2bff2e945e8547e273</citedby><cites>FETCH-LOGICAL-c321t-6b8a84cfdc318ca97fd1e06255a6afe6204a353d55bf3ba2bff2e945e8547e273</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27922,27923</link.rule.ids></links><search><creatorcontrib>Khamsi, M. A.</creatorcontrib><title>Generalized metric spaces: A survey</title><title>Journal of fixed point theory and applications</title><addtitle>J. Fixed Point Theory Appl</addtitle><description>Banach’s contraction mapping principle is remarkable in its simplicity, yet it is perhaps the most widely applied fixed point theorem in all of analysis with special applications to the theory of differential and integral equations. Because the underlined space of this theorem is a metric space, the theory that developed following its publication is known as the metric fixed point theory. Over the last one hundred years, many people have tried to generalize the definition of a metric space. In this paper, we survey the most popular generalizations and we discuss the recent uptick in some generalizations and their impact in metric fixed point theory.</description><subject>Analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1661-7738</issn><issn>1661-7746</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9j01LAzEURYMoWKs_wN2A6-h7-a67UrQKhW7qOmQyLzKlnZakFeqvd8qIS1fvLt653MPYPcIjAtingmid4oCag5CC6ws2QmOQW6vM5V-W7prdlLIGMCDQjtjDnDrKYdN-U1Nt6ZDbWJV9iFSeq2lVjvmLTrfsKoVNobvfO2Yfry-r2RtfLOfvs-mCRynwwE3tglMxNVGii2FiU4MERmgdTEhkBKggtWy0rpOsg6hTEjRRmpxWloSVY4ZDb8y7UjIlv8_tNuSTR_BnSz9Y-t7Sny297hkxMKX_7T4p-_XumLt-5j_QD1GyVBs</recordid><startdate>20150901</startdate><enddate>20150901</enddate><creator>Khamsi, M. A.</creator><general>Springer Basel</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20150901</creationdate><title>Generalized metric spaces: A survey</title><author>Khamsi, M. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c321t-6b8a84cfdc318ca97fd1e06255a6afe6204a353d55bf3ba2bff2e945e8547e273</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Khamsi, M. A.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of fixed point theory and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Khamsi, M. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized metric spaces: A survey</atitle><jtitle>Journal of fixed point theory and applications</jtitle><stitle>J. Fixed Point Theory Appl</stitle><date>2015-09-01</date><risdate>2015</risdate><volume>17</volume><issue>3</issue><spage>455</spage><epage>475</epage><pages>455-475</pages><issn>1661-7738</issn><eissn>1661-7746</eissn><abstract>Banach’s contraction mapping principle is remarkable in its simplicity, yet it is perhaps the most widely applied fixed point theorem in all of analysis with special applications to the theory of differential and integral equations. Because the underlined space of this theorem is a metric space, the theory that developed following its publication is known as the metric fixed point theory. Over the last one hundred years, many people have tried to generalize the definition of a metric space. In this paper, we survey the most popular generalizations and we discuss the recent uptick in some generalizations and their impact in metric fixed point theory.</abstract><cop>Basel</cop><pub>Springer Basel</pub><doi>10.1007/s11784-015-0232-5</doi><tpages>21</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1661-7738
ispartof Journal of fixed point theory and applications, 2015-09, Vol.17 (3), p.455-475
issn 1661-7738
1661-7746
language eng
recordid cdi_crossref_primary_10_1007_s11784_015_0232_5
source Springer Link
subjects Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
title Generalized metric spaces: A survey
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T09%3A10%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_sprin&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Generalized%20metric%20spaces:%20A%20survey&rft.jtitle=Journal%20of%20fixed%20point%20theory%20and%20applications&rft.au=Khamsi,%20M.%20A.&rft.date=2015-09-01&rft.volume=17&rft.issue=3&rft.spage=455&rft.epage=475&rft.pages=455-475&rft.issn=1661-7738&rft.eissn=1661-7746&rft_id=info:doi/10.1007/s11784-015-0232-5&rft_dat=%3Ccrossref_sprin%3E10_1007_s11784_015_0232_5%3C/crossref_sprin%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c321t-6b8a84cfdc318ca97fd1e06255a6afe6204a353d55bf3ba2bff2e945e8547e273%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true