A parallel hybrid method for equilibrium problems, variational inequalities and nonexpansive mappings in Hilbert space

Abstract

In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.

16 pages

References in corpus (4)

• Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis
• Regularization of systems of nonlinear ill-posed equations: II. Applications
• Parallel and sequential hybrid methods for a finite family of asymptotically quasi $\varphi$-nonexpansive mappings
• Parallel methods for regularizing systems of equations involving accretive operators

Cited by in corpus (7)

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• Parallel projection methods for variational inequalities involving common fixed point problems
• Parallel extragradient - viscosity methods for equilibrium problems and fixed point problems
• An extension of hybrid method without extrapolation step to equilibrium problems
• Hybrid algorithms without the extra-steps for equilibrium problems
• A novel hybrid method for equilibrium problems and fixed point problems
• Parallel extragradient-proximal methods for split equilibrium problems