In this paper, we present an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of an infinite family of nonexpansive mappings and the set of a variational inclusion in a real Hilbert space. Furthermore, we prove...

Let C be a nonempty closed convex subset of a uniformly convex and 2-uniformly smooth Banach space E and let Π<Subscript> C </Subscript> be a sunny nonexpansive retraction from E onto C. Let the mappings <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${T, S: C \to E}$$</EquationSource> </InlineEquation> be γ <Subscript>1</Subscript>-strongly accretive, μ <Subscript>1</Subscript>-Lipschitz continuous and γ <Subscript>2</Subscript>-strongly accretive, μ...</subscript></subscript></subscript></subscript></equationsource></inlineequation></subscript>

The purpose of this paper is to construct two superimposed optimization methods for solving the mixed equilibrium problem and variational inclusion. We show that the proposed superimposed methods converge strongly to a solution of some optimization problem. Note that our methods do not involve...