Let be a nonempty closed convex subset of a complete CAT (0) space and let be a nonexpansive nonself-mapping.
Let be a nonempty compact convex subset of a complete CAT (0) space and let be a nonexpansive nonself-mapping.
Let be a closed convex subset of a complete CAT 0) space, and let be a nonexpansive nonself-mapping.
One of the fundamental and celebrated results in the theory of nonexpansive mappingsis Browder's demiclosed principle[1] which states that if X is a uniformly convex Banach space,C is a nonempty closed convex subset of X, and if is a nonexpansive nonself mapping, then is demiclosed at 0, that is, for any sequence in C if weakly and, then (where I is the identity mapping inX).
where T : K → E is a nonexpansive nonself-mapping and K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P nonexpansive retraction.
Let E be a real Banach space, C be a nonempty closed convex subset of E and (P E rightarrow C) be a nonexpansive retraction of E onto E. Let (T Crightarrow E) be an asymptotically nonexpansive nonself-mapping.
Let K be a nonempty bounded closed convex subset of a complete CAT 0) space (X, d), P be a nonexpansive retraction of X onto K and (T Krightarrow X) be a uniformly continuous nearly asymptotically nonexpansive nonself mapping.
Let (kappa >0) and (X, d) be a complete CAT ((kappa )) space with diam ((X le frac{pi /2-epsilon }{sqrt{kappa }}) for some (epsilon in (0,pi /2).) Let K be a nonempty closed convex subset of X, P be a nonexpansive retraction of X onto K and (T Krightarrow X) be a uniformly continuous nearly asymptotically nonexpansive nonself mapping with (F(T ne emptyset).
Let C be a nonempty closed convex subset of a uniformly convex Banach space X and P : X → C be a nonexpansive retraction from X onto C. Let T1, T2, T3 : C → X be three continuous nonself mappings which are asymptotically nonexpansive in the intermediate sense.
