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Approximating solutions of variational inequalities for asymptotically nonexpansive mappings. (English) Zbl 1181.65098
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 KK, 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. C. Chidume, J. Li and A. Udomene, Proc. Am. Math. Soc. 133, No. 2, 473–480 (2005; Zbl 1073.47059)].
MSC:
65K15Numerical methods for variational inequalities and related problems
49J40Variational methods including variational inequalities
References:
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