q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems

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dc.contributor.authorKünzi, Hans-Peter A.
dc.contributor.authorOtafudu, Olivier Olela
dc.date.accessioned2022-04-21T11:26:27Z
dc.date.available2022-04-21T11:26:27Z
dc.date.issued2012-07-04
dc.descriptionIn a previous work, we started investigating a concept of hyperconvexity in quasipseudometric spaces, which we called q-hyperconvexity or Isbell-convexity (see [1], compare [2]). In this paper, we continue our studies of this concept by generalizing further known results about hyperconvexity from the metric setting to our theory.en_US
dc.description.abstractIn 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.)en_US
dc.description.sponsorshipThe South African National Research Foundation World Banken_US
dc.identifier.citationKünzi, H.P.A., Otafudu, O.O. (2012). q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems. Journal of Function Spaces and Applications Volume 2012, Article ID 765903, 18 pages doi:10.1155/2012/765903en_US
dc.identifier.urihttp://hdl.handle.net/123456789/1410
dc.language.isoenen_US
dc.publisherHindawi publishing Corporationen_US
dc.relation.ispartofseriesdoi:10.1155/2012/765903;18
dc.subjectq-Hyperconvexityen_US
dc.subjectQuasipseudometric Spaces Theoremen_US
dc.subjectFixed Point Theoremen_US
dc.titleq-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theoremsen_US
dc.typeArticleen_US
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