Approximation to fixed points of generalized nonexpansive mappings
Chi Song Wong · Proceedings of the American Mathematical Society · 1976
Let K K be a convex subset of a uniformly convex Banach space. It is proved that if K K is compact, then the fixed points of a continuous generalized nonexpansive self-mapping T T on K K can be approximated by the iterates of T t {T_t} with t ∈ ( 0 , 1 ) , T t ( x ) = ( 1 − t ) x + t T ( x ) , x ∈ K ; T t t \in (0,1),{T_t}(x) = (1 - t)x + tT(x),x \in K;{T_t} is asymptotically regular if T T has a fixed point.