Weak convergence theorems for a system of mixed equilibrium problems and nonspreading mappings in a Hilbert space. (English) Zbl 1189.47067

From the summary: We introduce an iterative sequence and prove a weak convergence theorem for finding a solution of a system of mixed equilibrium problems and the set of fixed points of a quasi-nonexpansive mapping in Hilbert spaces. Moreover, we apply our result to obtain a weak convergence theorem for finding a solution of a system of mixed equilibrium problems and the set of fixed points of a nonspreading mapping. Using this result, we improve and unify several results in fixed point problems and equilibrium problems.


47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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