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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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117129700094X |
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| author | Sehie Park |
| author_facet | Sehie Park |
| author_sort | Sehie Park |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a96145ceb2754663b37ffda17a8cf38f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a96145ceb2754663b37ffda17a8cf38f2025-02-03T05:58:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120468969810.1155/S016117129700094XExtensions of best approximation and coincidence theoremsSehie Park0Department of Mathematics, Seoul National University, Seoul 151–742, KoreaLet 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.http://dx.doi.org/10.1155/S016117129700094Xmultifunctionupper semicontinuous (u.s.c.)acyclicconvex spaceadmissible classbest approximationmetric projectioninward [outward] set. |
| spellingShingle | Sehie Park Extensions of best approximation and coincidence theorems International Journal of Mathematics and Mathematical Sciences multifunction upper semicontinuous (u.s.c.) acyclic convex space admissible class best approximation metric projection inward [outward] set. |
| title | Extensions of best approximation and coincidence theorems |
| title_full | Extensions of best approximation and coincidence theorems |
| title_fullStr | Extensions of best approximation and coincidence theorems |
| title_full_unstemmed | Extensions of best approximation and coincidence theorems |
| title_short | Extensions of best approximation and coincidence theorems |
| title_sort | extensions of best approximation and coincidence theorems |
| topic | multifunction upper semicontinuous (u.s.c.) acyclic convex space admissible class best approximation metric projection inward [outward] set. |
| url | http://dx.doi.org/10.1155/S016117129700094X |
| work_keys_str_mv | AT sehiepark extensionsofbestapproximationandcoincidencetheorems |