Strong convergence of an iterative procedure for pseudomonotone variational inequalities and fixed point problems

Strong convergence of a hybrid method for pseudomonotone variational inequalities and fixed point problems

In this paper, we suggest a hybrid method for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods: extragradient method and CQ method. We derive a necessary and sufficient condition f...

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 ...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Strong Convergence of an Iterative Method for Variational Inequality Problems and Fixed Point Problems

In this paper, we introduce a general iterative scheme to investigate the problem of finding a common element of the fixed point set of a strict pseudocontraction and the solution set of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Strong convergence theorems are established in a real Hilbert space.

A strong convergence theorem for solutions of zero point problems and fixed point problems

Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces‎.