Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings. (English) Zbl 1153.54024

Let \(C\) be a nonempty closed convex subset of a Hilbert space \(H\) and \(h: C\times C\to\mathbb{R}\) be an equilibrium bifunction, that is, \(h(u,u)= 0\) for every \(u\in C\). Then one can define the equilibrium problem that is to find an element \(u\in C\) such that \(h(u,v)\geq 0\) for all \(v\in C\).
In the present paper the authors introduce a new iterative scheme for finding (by strong convergence) a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of nonexpansive mappings in a Hilbert space.


54H25 Fixed-point and coincidence theorems (topological aspects)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
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