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Hybrid algorithms of common solutions of generalized mixed equilibrium problems and the common variational inequality problems with applications. (English) Zbl 1215.49014

Summary: We introduce new iterative algorithms by the hybrid method for finding a common element of the set of solutions of fixed points of infinite family of nonexpansive mappings, the set of common solutions of generalized mixed equilibrium problems, and the set of common solutions of the variational inequality with inverse-strongly monotone mappings in a real Hilbert space. We prove the strong convergence of the proposed iterative method under some suitable conditions. Finally, we apply our results to complementarity problems and optimization problems. Our results improve and extend the results announced by many others.

MSC:

49J40 Variational inequalities
47J25 Iterative procedures involving nonlinear operators
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