Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure

Fixed points of a certain class of mappings in spaces with uniformly normal structure

“…LEMMA (2), the result of Casini and Maluta [13], and the asymptotic regularity ofT, we have By (3) and (4) …”

Uniform asymptotic normal structure, the uniform semi‐Opial property and fixed points of asymptotically regular uniformly lipschitzian semigroups. Part I

“…James [5]. This is essentially the space which has been discussed in various places in the literature, e.g., [1,2,4,5,7,8,10,15,16,19,20,21,22,23,25,26,28,39].…”

“…The semi-Opial property was considered in the context of the fixed point property in product spaces [25]. To study more carefully the geometric structure of Banach spaces Bynum [9] introduced the normal structure coefficient N (X) which was applied by Casini and Maluta [10] to obtain a fixed point theorem for uniformly lipschitzian mappings. This result has been recently improved by Domínguez Benavides [15] .…”

Uniform asymptotic normal structure, the uniform semi‐Opialproperty, and fixed points of asymptotically regular uniformly lipschitzian semigroups. Part II

“…In each Banach space we have κ 0 (X) ≤ N (X) (see (1)) but in particular cases we can have κ 0 (X) < N (X) [7]. Therefore the following result is important.…”