Abstract
In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.
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Yao, Y., Cho, Y.J. & Liou, YC. Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems. centr.eur.j.math. 9, 640–656 (2011). https://doi.org/10.2478/s11533-011-0021-3
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DOI: https://doi.org/10.2478/s11533-011-0021-3