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On the normal structure coefficient and the bounded sequence coefficient


Author: Teck-Cheong Lim
Journal: Proc. Amer. Math. Soc. 88 (1983), 262-264
MSC: Primary 46B20; Secondary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1983-0695255-2
MathSciNet review: 695255
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Abstract: The two notions of normal structure coefficient and bounded sequence coefficient introduced by Bynum are shown to be the same. A lower bound for the normal structure coefficient in $ {L^p}$, $ p > 2$, is also given.


References [Enhancements On Off] (What's this?)

  • [1] W. L. Bynum, Normal structure coefficients for Banach spaces, Pacific J. Math. 86 (1980), 427-436. MR 590555 (81m:46030)
  • [2] R. B. Holmes, A course in optimization and best approximation, Lecture Notes in Math., vol. 257, Springer-Verlag, Berlin and New York, 1972. MR 0420367 (54:8381)
  • [3] T. C. Lim, Characterizations of normal structure, Proc. Amer. Math. Soc. 43 (1974), 313-319. MR 0361728 (50:14173)
  • [4] -, Fixed point theorems for uniformly Lipschitzian mappings in $ {L^p}$ spaces, J. Nonlinear Anal. Theory, Method and Appl. (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0695255-2
Keywords: Normal structure coefficient, bounded sequence coefficient, Chebyshev radius, asymptotic radius, inequality in $ {L^p}$
Article copyright: © Copyright 1983 American Mathematical Society

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