On Approximation of the Combination of Variational Inequality Problem and Equilibrium Problem for Nonlinear Mappings

Abstract

Using the concept of the combination of equilibrium problem, we introduce the combination of variational inequality problem for a finite family of inverse-strongly monotone mappings. Under some control conditions, we prove the strong convergence theorem for these nonlinear problems and fixed points of nonspreading mapping. Finally, we give numerical examples in two-dimensional space of real numbers in order to compare numerical results between the combination of variational inequality problem and the variational inequality problem.