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Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces
Fixed Point Theory and Applications volume 2006, Article number: 69758 (2006)
Abstract
Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm, let be a nonempty closed convex subset of , and let be a uniformly continuous pseudocontraction. If is any contraction map on and if every nonempty closed convex and bounded subset of has the fixed point property for nonexpansive self-mappings, then it is shown, under appropriate conditions on the sequences of real numbers , , that the iteration process , , , strongly converges to the fixed point of , which is the unique solution of some variational inequality, provided that is bounded.
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Udomene, A. Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces. Fixed Point Theory Appl 2006, 69758 (2006). https://doi.org/10.1155/FPTA/2006/69758
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DOI: https://doi.org/10.1155/FPTA/2006/69758