Inese Bula (2005)
Banach Center Publications
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The paper introduces a notion of strictly convex metric space and strictly convex metric space with round balls. These objects generalize the well known concept of strictly convex Banach space. We prove some fixed point theorems in strictly convex metric spaces with round balls.
J. Valentine (1978)
Fundamenta Mathematicae
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L. Loveland, J. Valentine (1978)
Fundamenta Mathematicae
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J. E. Valentine, S. G. Wayment (1973)
Colloquium Mathematicae
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Zajíček, L.
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B. Krakus (1972)
Fundamenta Mathematicae
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Tadeusz Dobrowolski, Jan van Mill (2006)
Fundamenta Mathematicae
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We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.
Ehrhard Behrends, Vladimir M. Kadets (2001)
Studia Mathematica
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A metric space (M,d) is said to have the small ball property (sbp) if for every ε₀ > 0 it is possible to write M as the union of a sequence (B(xₙ,rₙ)) of closed balls such that the rₙ are smaller than ε₀ and lim rₙ = 0. We study permanence properties and examples of sbp. The main results of this paper are the following: 1. Bounded convex closed sets in Banach spaces have sbp only if they are compact. 2. Precisely the finite-dimensional Banach spaces have sbp. (More generally: a complete...
Wulbert, D. E.
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Traoré, S., Volle, M. (1996)
Journal of Convex Analysis
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Huynh Van Ngai, Jean-Paul Penot (2008)
Studia Mathematica
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We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded....