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A new geometrical coefficient for Banach spaces and its applications in fixed point theory. (English) Zbl 0830.47041

The authors introduce a geometrical coefficient in Banach spaces which is related to E. A. Lifshits’ coefficient [Voronez. Gos. Univ. Trudy Mat. Fak. 16, 23-28 (1975)], but easier to compute. The new coefficient may be calculated explicitly, e.g., in \(\ell_p\) for \(1< p< \infty\). Applications to fixed point theory of uniformly Lipschitz mappings are given as well.

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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