Convergence theorems for fixed points of demicontinuous pseudocontractive mappings
CE Chidume, Habtu Zegeye · Fixed Point Theory and Applications · 2005
Abstract Let "Equation missing" be an open subset of a real uniformly smooth Banach space "Equation missing". Suppose "Equation missing" is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where "Equation missing" denotes the closure of "Equation missing". Then, it is proved that (i) "Equation missing" for every "Equation missing"; (ii) for a given "Equation missing", there exists a unique path "Equation missing", "Equation missing", satisfying "Equation missing". Moreover, if "Equation missing" or there exists "Equation missing" such that the set "Equation missing" is bounded, then it is proved that, as "Equation missing", the path "Equation missing" converges strongly to a fixed point of "Equation missing". Furthermore, explicit iteration procedures with bounded error terms are proved to converge strongly to a fixed point of "Equation missing".