Parallel hybrid methods for generalized equilibrium problems and asymptotically strictly pseudocontractive mappings

Abstract

In this paper, we propose two novel parallel hybrid methods for finding a common element of the set of solutions of a finite family of generalized equilibrium problems for monotone bifunctions $\left\{f_i\right\}_{i=1}^N$ and $\alpha$ - inverse strongly monotone operators $\left\{A_i\right\}_{i=1}^N$ and the set of common fixed points of a finite family of (asymptotically) $\kappa$- strictly pseudocontractive mappings $\left\{S_j\right\}_{j=1}^M$ in Hilbert spaces. The strong convergence theorems are established under the standard assumptions imposed on equilibrium bifunctions and operators. A numerical example is presented to illustrate the efficiency of the proposed parallel methods.