The construction of an asymptotic center with a fixed-point property

摘要: ABSTRACT. Given a bounded sequence {un: n = 1,2,...} of points in closed convex subset C uniformly Banach space, cm denotes the point with property that among all balls centered at and containing {um,um+lt...} one is smallest radius. It shown {cm: m converges (strongly) to ceC called asymptotic center {un} respect C. Further, for class mappings ƒ into itself, which contains nonexpansive mappings, f(c) c whenever an x e exists such "(x) «„,« 1,2,... .