Abstract
In this paper, we introduce a new iterative scheme for finding a common element of the set of common solutions of a finite family of equilibrium problems with relaxed monotone mappings, of the set of common solutions of a finite family of variational inequalities and of the set of common fixed points of an infinite family of nonexpansive mappings in a Hilbert space. Strong convergence for the proposed iterative scheme is proved. As an application, we solve a multi-objective optimization problem using the result of this paper. Our results improve and extend the corresponding ones announced by others.
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Wang, S., Marino, G. & Liou, YC. Strong convergence theorems for variational inequality, equilibrium and fixed point problems with applications. J Glob Optim 54, 155–171 (2012). https://doi.org/10.1007/s10898-011-9754-6
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DOI: https://doi.org/10.1007/s10898-011-9754-6