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Some resolvent iterative methods for variational inclusions and nonexpansive mappings. (English) Zbl 1193.49010
Summary: We suggest and analyze three-step iterations for finding the common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions using the resolvent operator technique. We also study the convergence criteria of three-step iterative method under some mild conditions. Our results include the previous results of the authors [J. Math. Anal. Appl. 331, No. 2, 810--822 (2007; Zbl 1112.49013); Appl. Math. Comput. 187, No. 2, 680--685 (2007; Zbl 1128.65050)] as special cases and may be considered as an improvement and refinement of the previously known results.

MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
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References:
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