q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems
In a previous work, we started investigating the concept of hyperconvexity in quasipseudometric spaces which we called q-hyperconvexity or Isbell-convexity. In this paper, we continue our studies of this concept, generalizing further known results about hyperconvexity from the metric setting to our...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/765903 |
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| author | Hans-Peter A. Künzi Olivier Olela Otafudu |
| author_facet | Hans-Peter A. Künzi Olivier Olela Otafudu |
| author_sort | Hans-Peter A. Künzi |
| collection | DOAJ |
| description | In a previous work, we started investigating the concept of hyperconvexity in quasipseudometric spaces which we called q-hyperconvexity or Isbell-convexity. In this paper, we continue our studies of this concept, generalizing further known results about hyperconvexity from the metric setting to our theory. In particular, in the present paper, we consider subspaces of q-hyperconvex spaces and also present some fixed point theorems for nonexpansive self-maps on a bounded q-hyperconvex quasipseudometric space. In analogy with a metric result, we show among other things that a set-valued mapping T∗ on a q-hyperconvex T0-quasimetric space (X, d) which takes values in the space of nonempty externally q-hyperconvex subsets of (X, d) always has a single-valued selection T which satisfies d(T(x),T(y))≤dH(T∗(x),T∗(y)) whenever x,y∈X. (Here, dH denotes the usual (extended) Hausdorff quasipseudometric determined by d on the set 𝒫0(X) of nonempty subsets of X.) |
| format | Article |
| id | doaj-art-dbbbf71c6b7b42f49899e8cf3d4a60f1 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-dbbbf71c6b7b42f49899e8cf3d4a60f12025-02-03T06:07:30ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/765903765903q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point TheoremsHans-Peter A. Künzi0Olivier Olela Otafudu1Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South AfricaDepartment of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South AfricaIn a previous work, we started investigating the concept of hyperconvexity in quasipseudometric spaces which we called q-hyperconvexity or Isbell-convexity. In this paper, we continue our studies of this concept, generalizing further known results about hyperconvexity from the metric setting to our theory. In particular, in the present paper, we consider subspaces of q-hyperconvex spaces and also present some fixed point theorems for nonexpansive self-maps on a bounded q-hyperconvex quasipseudometric space. In analogy with a metric result, we show among other things that a set-valued mapping T∗ on a q-hyperconvex T0-quasimetric space (X, d) which takes values in the space of nonempty externally q-hyperconvex subsets of (X, d) always has a single-valued selection T which satisfies d(T(x),T(y))≤dH(T∗(x),T∗(y)) whenever x,y∈X. (Here, dH denotes the usual (extended) Hausdorff quasipseudometric determined by d on the set 𝒫0(X) of nonempty subsets of X.)http://dx.doi.org/10.1155/2012/765903 |
| spellingShingle | Hans-Peter A. Künzi Olivier Olela Otafudu q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems Journal of Function Spaces and Applications |
| title | q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems |
| title_full | q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems |
| title_fullStr | q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems |
| title_full_unstemmed | q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems |
| title_short | q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems |
| title_sort | q hyperconvexity in quasipseudometric spaces and fixed point theorems |
| url | http://dx.doi.org/10.1155/2012/765903 |
| work_keys_str_mv | AT hanspeterakunzi qhyperconvexityinquasipseudometricspacesandfixedpointtheorems AT olivierolelaotafudu qhyperconvexityinquasipseudometricspacesandfixedpointtheorems |