Strongly Convergent Algorithms for Variational Inequality Problem Over the Set of Solutions the Equilibrium Problems

Abstract

AbstractThis chapter deals with a variational inequality problem over the set of solutions the equilibrium problem or over the set of solutions the system of equilibrium problems in a real Hilbert space. Several new iterative algorithms are proposed. Strong convergence theorems for algorithms are proved. The convergence of iterative algorithms with the presence of computational errors without traditional summability conditions also studied. To this aim, we use new Mainge’s techniques for analysis non–Fejerian iterative processes (Set–Valued Analysis. 16, 899–912, 2008).KeywordsVariational Inequality ProblemEquilibrium ProblemStrong Convergence TheoremMaingiComputational ErrorsThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.