Extensions of best approximation and coincidence theorems
Let X be a Hausdorff compact space, E a topological vector space on which E* separates points, F:X→2E an upper semicontinuous multifunction with compact acyclic values, and g:X→E a continuous function such that g(X) is convex and g−1(y) is acyclic for each y∈g(X). Then either (1) there exists an x0∈...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129700094X |
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| Summary: | Let X be a Hausdorff compact space, E a topological vector space on which E* separates points, F:X→2E an upper semicontinuous multifunction with compact acyclic
values, and g:X→E a continuous function such that g(X) is convex and g−1(y) is acyclic for
each y∈g(X). Then either (1) there exists an x0∈X such that gx0∈Fx0 or (2) there exist an (x0,z0) on the graph of F and a continuous seminorm p on E such that 0<p(gx0−z0)≤p(y−z0) for all y∈g(X). A generalization of this result and its application to coincidence theorems are obtained. Our
aim in this paper is to unify and improve almost fifty known theorems of others. |
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| ISSN: | 0161-1712 1687-0425 |