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Continuity properties of projection operators

Abstract

We prove that the projection operator on a nonempty closed convex subset of a uniformly convex Banach spaces is uniformly continuous on bounded sets and we provide an estimate of its modulus of uniform continuity. We derive this result from a study of the dependence of the projection on of a given point when varies.

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Correspondence to Jean-Paul Penot.

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Penot, JP. Continuity properties of projection operators. J Inequal Appl 2005, 921970 (2005). https://doi.org/10.1155/JIA.2005.509

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  • DOI: https://doi.org/10.1155/JIA.2005.509