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On the uniform continuity of metric projections in Banach spaces

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Approximation Theory and its Applications

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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Authors and Affiliations

  1. Department of Mathematics, Xi'an Jiaotong University, 710049, Xi'an, PRC

    Xu Zongben

  2. Department of Mathematics, University of Strathelyde, Glasgow, U.K.

    G. F. Roach

Authors
  1. Xu Zongben
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  2. G. F. Roach
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Zongben, X., Roach, G.F. On the uniform continuity of metric projections in Banach spaces. Approx. Theory & its Appl. 8, 11–20 (1992). https://doi.org/10.1007/BF02836334

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  • DOI: https://doi.org/10.1007/BF02836334

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