Equilibrium programming using proximal-like algorithms
Mathematical Programming: Series A and B
A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces
Mathematics of Operations Research
A hybrid iterative scheme for mixed equilibrium problems and fixed point problems
Journal of Computational and Applied Mathematics
Convergence theorems for nonexpansive mappings and feasibility problems
Mathematical and Computer Modelling: An International Journal
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We prove the existence of a solution of the mixed equilibrium problem (MEP) by using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solutions set of a mixed equilibrium problem and the fixed points set of a countable family of nonexpansive mappings in the frameworks of Banach spaces. By using a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solutions set of MEP and common fixed points set of nonexpansive mappings. Moreover, some applications concerning the equilibrium and the convex minimization problems are obtained.