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 sh...
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th-cmuir.6653943832-50922014-08-30T02:56:09Z Fixed points of uniformly lipschitzian mappings Dhompongsa S. Kirk W.A. Sims B. 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. © 2005. 2014-08-30T02:56:08Z 2014-08-30T02:56:08Z 2006 Article 0362546X 10.1016/j.na.2005.09.044 NOAND http://www.scopus.com/inward/record.url?eid=2-s2.0-33646854043&partnerID=40&md5=57dccc557d547ed48848b065ec947555 http://cmuir.cmu.ac.th/handle/6653943832/5092 English |
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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. © 2005. |
| format |
Article |
| author |
Dhompongsa S. Kirk W.A. Sims B. |
| spellingShingle |
Dhompongsa S. Kirk W.A. Sims B. Fixed points of uniformly lipschitzian mappings |
| author_facet |
Dhompongsa S. Kirk W.A. Sims B. |
| author_sort |
Dhompongsa S. |
| title |
Fixed points of uniformly lipschitzian mappings |
| title_short |
Fixed points of uniformly lipschitzian mappings |
| title_full |
Fixed points of uniformly lipschitzian mappings |
| title_fullStr |
Fixed points of uniformly lipschitzian mappings |
| title_full_unstemmed |
Fixed points of uniformly lipschitzian mappings |
| title_sort |
fixed points of uniformly lipschitzian mappings |
| publishDate |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-33646854043&partnerID=40&md5=57dccc557d547ed48848b065ec947555 http://cmuir.cmu.ac.th/handle/6653943832/5092 |
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1681420360111620096 |