AVERAGED ITERATES FOR NON-EXPANSIVE NONSELF-MAPPINGS IN BANACH SPACES
Let E be a uniformly convex Banach space with a uniformly Gateaux differentiable norm and K be a closed convex subset of E which is also a sunny non-expansive retract of E. Assume that T : K E is a nonexpansive mappings with a fixed point. The two averaged iterative sequences {x(n)} are given by [GRAPHICS] where P is sunny non-expansive retraction of E onto K and alpha n is an element of (0, 1) satisfying the conditions: lim(n ->infinity) alpha(n) = 0 and Sigma(infinity)(n=0) alpha(n)=infinity. We prove that {x(n)} converges strongly to some fixed point of T and, furthermore, as applications, we obtain the viscosity averaged approximation results for T.
averaged iterates non-expansive nonself-mappings uniformly convex banach space