On the uniform continuity of metric projections in Banach spaces

Xu Zongben; G. F. Roach

doi:10.1007/BF02836334

On the uniform continuity of metric projections in Banach spaces

Xu Zongben
, G. F. Roach

School of Mathematics and Statistics

University of Strathclyde

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

Let M be a convex Chebyshev subset of a uniformly convex and uniformly smooth Banach space. It is proved that the metric projection P_M of X onto M is uniformly continuous on every bounded subset of X. Moreover, a global and explicit estimate on the modulus of continuity of the metric projection is obtained.

Original language	English
Pages (from-to)	11-20
Number of pages	10
Journal	Approximation Theory and Its Applications
Volume	8
Issue number	3
DOIs	https://doi.org/10.1007/BF02836334
State	Published - Sep 1992

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title = "On the uniform continuity of metric projections in Banach spaces",

abstract = "Let M be a convex Chebyshev subset of a uniformly convex and uniformly smooth Banach space. It is proved that the metric projection PM of X onto M is uniformly continuous on every bounded subset of X. Moreover, a global and explicit estimate on the modulus of continuity of the metric projection is obtained.",

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AB - Let M be a convex Chebyshev subset of a uniformly convex and uniformly smooth Banach space. It is proved that the metric projection PM of X onto M is uniformly continuous on every bounded subset of X. Moreover, a global and explicit estimate on the modulus of continuity of the metric projection is obtained.

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On the uniform continuity of metric projections in Banach spaces

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