Approximating solutions of variational inequalities for asymptotically nonexpansive mappings
Let \(E\) be a real Banach space with a uniformly Gâteaux differentiable norm and possessing a uniform normal structure. Iterative sequences are constructed which involve a contractive and an asymptotically nonexpanding mappings \(K\to K\), where \(K\) is a bounded closed convex subset of \(E\). Conditions are given for convergence of these sequences to a fixed point which is also the unique solution of some variational inequalities. Thus previous results on asymptotically nonexpanding mappings are generalized [see e.g. \textit{C.~Chidume, J.~Li} and \textit{A.~Udomene}, Proc. Am. Math. Soc. 133, No.~2, 473--480 (2005; Zbl 1073.47059)].
scientific article; zbMATH DE number 5569540