Convergence analysis for the equilibrium problems with numerical results

Abstract

In this paper, we propose an iterative scheme modified from the work of Ceng et al. (Nonlinear Anal. Hybrid Syst. 4:743-754, 2010) and Plubtieng and Punpaeng (J. Math. Anal. Appl. 336(1):455-469, 2007) to prove the strong convergence theorem for approximating a common element of the set of fixed points of nonspreading mappings and a finite family of the set of solutions of the equilibrium problem. Using this result, we obtain the strong convergence theorem for a finite family of nonspreading mappings and a finite family of the set of solutions of equilibrium problem. Moreover, in order to compare numerical results between the combination of the equilibrium problem and the classical equilibrium problem, some examples are given in one- and two-dimensional spaces of real numbers.