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Convergence theorems for fixed points of demicontinuous pseudocontractive mappings
Fixed Point Theory and Applications volume 2005, Article number: 475373 (2005)
Abstract
Let be an open subset of a real uniformly smooth Banach space . Suppose is a demicontinuous pseudocontractive mapping satisfying an appropriate 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 proved to converge strongly to a fixed point of .
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Chidume, C., Zegeye, H. Convergence theorems for fixed points of demicontinuous pseudocontractive mappings. Fixed Point Theory Appl 2005, 475373 (2005). https://doi.org/10.1155/FPTA.2005.67
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DOI: https://doi.org/10.1155/FPTA.2005.67