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
N. M. Gulevich, S. V. Konyagin, and R. V. Rakhmankulov, “Fixed points and differentiability of norms,”Mat. Sb.,136, 468–477 (1988).
N. M. Gulevich, “The measure of nonconvexity and the Jung constant,” this volume.
N. Dunford and J. T. Schwartz,Linear Operators. Part I: General Theory, Yale University, Intersci. Publ., New York-London (1958).
S. A. Pichugov, “The Jung constant of theL p space,”Mat. Zametki,43, 604–614 (1988).
Additional information
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