The purpose of this paper is using Korpelevich’s extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approxima...

In this paper, we use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our method includes the two-step forward-backward splitting and extragradient methods for solving various cl...

We consider the forward-backward splitting method for nding a zero of the sum of two maximal monotone mappings. This method is known to converge when the inverse of the forward mapping is strongly monotone. We propose a modiication to this method, in the spirit of the extragradient method for monotone variational inequalities, under which the method converges assuming only the forward mapping i...

‎in this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎the first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎the second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎....

A new framework for analyzing Fejér convergent algorithms is presented. Using this framework we define a very general class of Fejér convergent algorithms and establish its convergence properties. We also introduce a new definition of approximations of resolvents which preserve some useful features of the exact resolvent, and use this concept to present an unifying view of the Forward-Backward ...