Convergence theorems for fixed points of demicontinuous pseudocontractive mappings

Convergence theorems for fixed points of demicontinuous pseudocontractive mappings

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Let be an open subset of a real uniformly smooth Banach space.Suppose is a demicontinuous pseudocontractive mapping satisfying an appropriate Horse Turnout Rugs condition, where denotes the closure of.Then, it is proved that (i) for every ; (ii) for a given , there exists a unique path , , satisfying.

Moreover, if or there exists such that the set is bounded, then it is proved that, as , the path converges strongly to a fixed point of.Furthermore, explicit iteration procedures with bounded error terms are Cramp Bark proved to converge strongly to a fixed point of.