# An Iterative Method for a Common Solution of a Combination of the Split Equilibrium Problem, a Finite Family of Nonexpansive Mapping and a Combination of Variational Inequality Problem

## DOI:

https://doi.org/10.5556/j.tkjm.52.2021.3563## Keywords:

Split equilibrium problem; variational inequality problem; fixed point problem; projection method; nonexpansive mapping.## Abstract

The present paper aims to deal with an iterative algorithm for finding common solution of the combination of the split equilibrium problem and a finite family of non-expansive mappings and the combination of variational inequality problem in the setting of real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution to these problems. A numerical example is presented to illustrate the proposed method and convergence result. The results and method presented in this paper generalize, extend and unify some known results in the literatures.

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*Tamkang Journal of Mathematics*,

*52*(3), 413-441. https://doi.org/10.5556/j.tkjm.52.2021.3563

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