On the normal structure coefficient and the bounded sequence coefficient. (English) Zbl 0541.46017
The two notions of normal structure coefficient N(X) and bounded sequence coefficient BS(X) introduced in W. L. Bynum [Pac. J. Math. 86, 427- 436 (1980; Zbl 0442.46018)] as well as the notion of asymptotic coefficient A(X) introduced by the author [Proc. Math. Soc. 43, 313-319 (1974; Zbl 0284.47031)] are shown to be the same in any Banach space X. A lower bound for N(X) in \(L^ p\), \(p>2\), is also given.
Reviewer: M.Turinici
MSC:
| 46B20 | Geometry and structure of normed linear spaces |
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 52A05 | Convex sets without dimension restrictions (aspects of convex geometry) |
Keywords:
Chebyshev radius; normal structure coefficient; bounded sequence coefficient; asymptotic coefficientReferences:
| [1] | W. L. Bynum, Normal structure coefficients for Banach spaces, Pacific J. Math. 86 (1980), no. 2, 427 – 436. · Zbl 0442.46018 |
| [2] | Richard B. Holmes, A course on optimization and best approximation, Lecture Notes in Mathematics, Vol. 257, Springer-Verlag, Berlin-New York, 1972. · Zbl 0235.41016 |
| [3] | Teck Cheong Lim, Characterizations of normal structure, Proc. Amer. Math. Soc. 43 (1974), 313 – 319. · Zbl 0284.47031 |
| [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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