A variant of a fixed point theorem of Browder-Fan and Reich
Let S be a convex, weakly compact subset of a locally convex Hausdorff space (E,τ) and f:S→E be a continuous multifunction from its weak topology ω to τ. let ρ be a continuous seminorm on (E,τ) and for subsets A, B of E let p(A,B)=inf{p(x−y):x ϵ A, y ϵ B}. In this paper, sufficient conditions are de...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000771 |
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| _version_ | 1832566968110022656 |
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| author | V. M. Sehgal |
| author_facet | V. M. Sehgal |
| author_sort | V. M. Sehgal |
| collection | DOAJ |
| description | Let S be a convex, weakly compact subset of a locally convex Hausdorff space (E,τ) and f:S→E be a continuous multifunction from its weak topology ω to τ. let ρ be a continuous seminorm on (E,τ) and for subsets A, B of E let p(A,B)=inf{p(x−y):x ϵ A, y ϵ B}. In this paper, sufficient conditions are developed for the existence of an x ϵ S satisfying p(x,fx)=p(fx,S). The result is then used to prove several fixed point theorems. |
| format | Article |
| id | doaj-art-8dfc1a3e7f7b49c5b9b5be938d158bd1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8dfc1a3e7f7b49c5b9b5be938d158bd12025-02-03T01:02:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018469369610.1155/S0161171285000771A variant of a fixed point theorem of Browder-Fan and ReichV. M. Sehgal0Department of Mathematics, University of Wyoming, Laramie 82071, Wyoming, USALet S be a convex, weakly compact subset of a locally convex Hausdorff space (E,τ) and f:S→E be a continuous multifunction from its weak topology ω to τ. let ρ be a continuous seminorm on (E,τ) and for subsets A, B of E let p(A,B)=inf{p(x−y):x ϵ A, y ϵ B}. In this paper, sufficient conditions are developed for the existence of an x ϵ S satisfying p(x,fx)=p(fx,S). The result is then used to prove several fixed point theorems.http://dx.doi.org/10.1155/S0161171285000771Multifunctionsconvex topologyfixed points. |
| spellingShingle | V. M. Sehgal A variant of a fixed point theorem of Browder-Fan and Reich International Journal of Mathematics and Mathematical Sciences Multifunctions convex topology fixed points. |
| title | A variant of a fixed point theorem of Browder-Fan and Reich |
| title_full | A variant of a fixed point theorem of Browder-Fan and Reich |
| title_fullStr | A variant of a fixed point theorem of Browder-Fan and Reich |
| title_full_unstemmed | A variant of a fixed point theorem of Browder-Fan and Reich |
| title_short | A variant of a fixed point theorem of Browder-Fan and Reich |
| title_sort | variant of a fixed point theorem of browder fan and reich |
| topic | Multifunctions convex topology fixed points. |
| url | http://dx.doi.org/10.1155/S0161171285000771 |
| work_keys_str_mv | AT vmsehgal avariantofafixedpointtheoremofbrowderfanandreich AT vmsehgal variantofafixedpointtheoremofbrowderfanandreich |