Fixed points of uniformly lipschitzian mappings
Two fixed point theorems for uniformly lipschitzian mappings in metric spaces, due respectively to E. Lifšic and to T.-C. Lim and H.-K. Xu, are compared within the framework of the so-called CAT(0) spaces. It is shown that both results apply in this setting, and that Lifšic’s theorem gives a sharper...
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| Veröffentlicht in: | Nonlinear analysis 2006-08, Vol.65 (4), p.762-772 |
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| container_title | Nonlinear analysis |
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| creator | Dhompongsa, S. Kirk, W.A. Sims, Brailey |
| description | Two fixed point theorems for uniformly lipschitzian mappings in metric spaces, due respectively to E. Lifšic and to T.-C. Lim and H.-K. Xu, are compared within the framework of the so-called CAT(0) spaces. It is shown that both results apply in this setting, and that Lifšic’s theorem gives a sharper result. Also, a new property is introduced that yields a fixed point theorem for uniformly lipschitzian mappings in a class of hyperconvex spaces, a class which includes those possessing property
(
P
)
of Lim and Xu. |
| doi_str_mv | 10.1016/j.na.2005.09.044 |
| format | Article |
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(
P
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(
P
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of Lim and Xu.</description><subject>CAT spaces</subject><subject>Exact sciences and technology</subject><subject>Fixed points</subject><subject>General topology</subject><subject>Hyperconvex spaces</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Operator theory</subject><subject>Sciences and techniques of general use</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><subject>Uniformly lipschitzian mappings</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNp1kL1PwzAUxC0EEqWwM2aBLam_YidsqKKAhMQCEpv16tjgKrGDnSLKX0-iVmJiesvd794dQpcEFwQTsdgUHgqKcVngusCcH6EZqSTLS0rKYzTDTNC85OLtFJ2ltMEYE8nEDC1W7ts0WR-cH1IWbLb1zobYtbusdX3SH274ceCzDvre-fd0jk4stMlcHO4cva7uXpYP-dPz_ePy9inXnJIh16LifC0tFwSgbkpjqaZsLWpJSw6GsTVUNasaypuKCVYTRgVIS6SkMHZgbI6u99w-hs-tSYPqXNKmbcGbsE2K1iOolJMQ74U6hpSisaqProO4UwSraRm1UR7UtIzCtRqXGS1XBzYkDa2N4LVLfz45voTxhL7Z68xY9MuZqJJ2xmvTuGj0oJrg_g_5Bdwadlc</recordid><startdate>20060801</startdate><enddate>20060801</enddate><creator>Dhompongsa, S.</creator><creator>Kirk, W.A.</creator><creator>Sims, Brailey</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20060801</creationdate><title>Fixed points of uniformly lipschitzian mappings</title><author>Dhompongsa, S. ; Kirk, W.A. ; Sims, Brailey</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c421t-c6844b7f461aa9d5ef2c23b697254ae33ba8938d24d836391326a7f1772a00533</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>CAT spaces</topic><topic>Exact sciences and technology</topic><topic>Fixed points</topic><topic>General topology</topic><topic>Hyperconvex spaces</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Operator theory</topic><topic>Sciences and techniques of general use</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><topic>Uniformly lipschitzian mappings</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dhompongsa, S.</creatorcontrib><creatorcontrib>Kirk, W.A.</creatorcontrib><creatorcontrib>Sims, Brailey</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dhompongsa, S.</au><au>Kirk, W.A.</au><au>Sims, Brailey</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fixed points of uniformly lipschitzian mappings</atitle><jtitle>Nonlinear analysis</jtitle><date>2006-08-01</date><risdate>2006</risdate><volume>65</volume><issue>4</issue><spage>762</spage><epage>772</epage><pages>762-772</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>Two fixed point theorems for uniformly lipschitzian mappings in metric spaces, due respectively to E. Lifšic and to T.-C. Lim and H.-K. Xu, are compared within the framework of the so-called CAT(0) spaces. It is shown that both results apply in this setting, and that Lifšic’s theorem gives a sharper result. Also, a new property is introduced that yields a fixed point theorem for uniformly lipschitzian mappings in a class of hyperconvex spaces, a class which includes those possessing property
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| ispartof | Nonlinear analysis, 2006-08, Vol.65 (4), p.762-772 |
| issn | 0362-546X 1873-5215 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | CAT spaces Exact sciences and technology Fixed points General topology Hyperconvex spaces Mathematical analysis Mathematics Operator theory Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Uniformly lipschitzian mappings |
| title | Fixed points of uniformly lipschitzian mappings |
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