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.

18 pages, Journal of Applied Mathematics and Computing (2016), Hybrid method, Equilibrium problem, Strictly pseudocontractive mapping, Parallel computation

References in corpus (6)

• Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings
• Parallel hybrid iterative methods for variational inequalities, equilibrium problems and common fixed point problems
• Parallel and sequential hybrid methods for a finite family of asymptotically quasi $\varphi$-nonexpansive mappings
• A parallel hybrid method for equilibrium problems, variational inequalities and nonexpansive mappings in Hilbert space
• Parallel methods for regularizing systems of equations involving accretive operators
• The common solutions to pseudomonotone equilibrium problems

Cited by in corpus (1)

• Parallel extragradient - viscosity methods for equilibrium problems and fixed point problems