Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

iterative methods for equilibrium problems, variational inequalities and fixed points

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

and Applied Analysis 3 where A n = α n I + A for all n ≥ 0. In particular, if V ≡ 0, then (11) reduces to the following iterative scheme: x 0 = x ∈ C chosen arbitrarily, y n = P C (x n − ] n A n x n ) , z n = β n x n + γ n P C (x n − ] n A n y n ) + σ n TP C (x n − ] n A n y n ) , x n+1 = P C [λ n (1 − δ n ) γSx n + (I − λ n μF) z n ] , ∀n ≥ 0. (12) Further, if S = V, then (11) reduces to the f...

A General Iterative Algorithm for Generalized Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities

We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the a...