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An estimate for the distance from a fixed-point set

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Abstract

An estimate for the distance between a bounded set B in a uniformly smooth Banach space and the fixed-point set of a nonexpanding mapping T is given. It is assumed that an iteration of T properly takes into B the set of extremal points of B. Bibliography: 4 titles.

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Literature Cited

  1. N. M. Gulevich, S. V. Konyagin, and R. V. Rakhmankulov, “Fixed points and differentiability of norms,”Mat. Sb.,136, 468–477 (1988).

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  2. N. M. Gulevich, “The measure of nonconvexity and the Jung constant,” this volume.

  3. N. Dunford and J. T. Schwartz,Linear Operators. Part I: General Theory, Yale University, Intersci. Publ., New York-London (1958).

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  4. S. A. Pichugov, “The Jung constant of theL p space,”Mat. Zametki,43, 604–614 (1988).

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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 208, 1993, pp. 182–185.

Translated by O. A. Ivanov.

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Gulevich, N.M. An estimate for the distance from a fixed-point set. J Math Sci 81, 2567–2569 (1996). https://doi.org/10.1007/BF02362427

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  • DOI: https://doi.org/10.1007/BF02362427

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