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On Bynum’s fixed point theorem. (English) Zbl 0724.46020

It was proved by Dan Amir in Pac. J. Math. 118, 1-15 (1985; Zbl 0529.46011), that the product of W. L. Bynum’s Banach space characteristic WCS(X) [Pac. J. Math. 86, 427-436 (1980; Zbl 0442.46018)] and E. Maluta’s characteristic D(X) [Pac. J. Math. 111, 357-369 (1984; Zbl 0495.46012)] is 1 for some class of spaces X. The author shows that this is true in general. Explicit calculation of \(WCS(L_ p)\) and \(WCS(\ell_ p)\) is also given.

MSC:

46B20 Geometry and structure of normed linear spaces
47H10 Fixed-point theorems

Keywords:

characteristic
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