A hybrid projection algorithm for finding solutions of mixed equilibrium problem and variational inequality problem.(English)Zbl 1203.47043

Summary: We propose a modified hybrid projection algorithm to approximate a common fixed point of a $$k$$-strict pseudocontraction and of two sequences of nonexpansive mappings. We prove a strong convergence theorem of the proposed method and we obtain, as a particular case, approximation of solutions of systems of two equilibrium problems.

MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 49J40 Variational inequalities
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