q -Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems
Joint Authors
Künzi, Hans-Peter A.
Olela Otafudu, Olivier
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-13
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
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 ?0(X) of nonempty subsets of X.)
American Psychological Association (APA)
Künzi, Hans-Peter A.& Olela Otafudu, Olivier. 2012. q -Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems. Journal of Function Spaces،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-994250
Modern Language Association (MLA)
Künzi, Hans-Peter A.& Olela Otafudu, Olivier. q -Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems. Journal of Function Spaces No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-994250
American Medical Association (AMA)
Künzi, Hans-Peter A.& Olela Otafudu, Olivier. q -Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems. Journal of Function Spaces. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-994250
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-994250