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Strong convergence theorems for variational inequalities and fixed point problems of asymptotically strict pseudocontractive mappings in the intermediate sense. (English) Zbl 1220.47086
Summary: The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce a modified hybrid Mann iterative scheme with perturbed mapping which is based on well-known CQ method, Mann iteration method and hybrid (or outer approximation) method. We establish a strong convergence theorem for three sequences generated by this modified hybrid Mann iterative scheme with perturbed mapping. Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47J20Inequalities involving nonlinear operators
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References:
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