Iterative fixed points of non-Lipschitzian self-mappings
Tae-Hwa Kim, Eun Suk Kim · Kodai Mathematical Journal · 1995
In this paper, we shall establish iterative fixed points of non-Lipschitzian continuous self-mappings on Banach spaces with weak uniform normal structure.In particular, T is said to be asymptotically nonexpansive [7] if lim n _oo & (rc)-1 and it is said to be nonexpansive if k(n)=l for any n<=N.We now consider a non-Lipschitzian self-mapping on C, that is to say, a mapping of weakly asymptotically nonexpansive type.We say that a mapping T: C-+C is said to be weakly asymptotically nonexpansive type (simply, w.a.n.t.) on C (see [10]) if, for each xeC and each bounded subset D of C, Immediately, we can see that all mappings of w.a.n.t.include all mappings of asymptotically nonexpansive type (see [11]).In particular, if T: C-+C is a Lipschitzian mapping with an additional condition, i.e., limsuρ n _oo k(ή)^l (see [12] and [14]), then it is obviously a continuous mapping of w.a.n.t.Further if C is bounded, then any mapping of w.a.n.t. is asymptotically nonexpansive type.