Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property. (English) Zbl 0849.47030

Bruck, Ronald; Kuczumow, Tadeusz; Reich, Simeon

Colloq. Math. 65, No. 2, 169-179 (1993).

The authors study asymptotically nonexpensive mappings in the intermediate sense, \(T: C\to C\), on a not necessarily convex subset \(C\) of a Banach space with the Opial condition, \(X\), i.e. \[ \limsup_{n\to \infty} \sup_{x,y\in C} (|T^n x- T^n y|- |x-y |)\leq 0. \] For such maps fixed points are constructed.

MSC:

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

Keywords:

asymptotically nonexpensive mappings in the intermediate sense; Banach space with the Opial condition; fixed points