Fixed point theorems for a sum of two mappings in locally convex spaces
Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contra...
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171294000967 |
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| author | P. Vijayaraju |
| author_facet | P. Vijayaraju |
| author_sort | P. Vijayaraju |
| collection | DOAJ |
| description | Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings. In this paper, we prove by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces. These results extend a result of Cain and Nashed. |
| format | Article |
| id | doaj-art-ca4c4e9a97474c75972b073c63ca868f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ca4c4e9a97474c75972b073c63ca868f2025-02-03T07:24:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117468168610.1155/S0161171294000967Fixed point theorems for a sum of two mappings in locally convex spacesP. Vijayaraju0Department of Mathematics, Anna University, Madras 600 025, IndiaCain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings. In this paper, we prove by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces. These results extend a result of Cain and Nashed.http://dx.doi.org/10.1155/S0161171294000967asymptotically nonexpansive and continuous mappingsuniformly asymptotically regular with respect to a map. |
| spellingShingle | P. Vijayaraju Fixed point theorems for a sum of two mappings in locally convex spaces International Journal of Mathematics and Mathematical Sciences asymptotically nonexpansive and continuous mappings uniformly asymptotically regular with respect to a map. |
| title | Fixed point theorems for a sum of two mappings in locally convex spaces |
| title_full | Fixed point theorems for a sum of two mappings in locally convex spaces |
| title_fullStr | Fixed point theorems for a sum of two mappings in locally convex spaces |
| title_full_unstemmed | Fixed point theorems for a sum of two mappings in locally convex spaces |
| title_short | Fixed point theorems for a sum of two mappings in locally convex spaces |
| title_sort | fixed point theorems for a sum of two mappings in locally convex spaces |
| topic | asymptotically nonexpansive and continuous mappings uniformly asymptotically regular with respect to a map. |
| url | http://dx.doi.org/10.1155/S0161171294000967 |
| work_keys_str_mv | AT pvijayaraju fixedpointtheoremsforasumoftwomappingsinlocallyconvexspaces |