We study and introduce modified mann iterative algorithms for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of variational inequalities and the set of fixed points for nonexpansive semigroups. Then, we prove strong convergence theorems in a real Hilbert space by using the hybrid-extragradient type methods in the mathematical programm...

This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the standard HPE method applied to regularizations of the original MIP. It is shown that its pointwise iteration-complexity considerably improves the one of the H...

In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse strongly monotone mapping. We prove a strong convergence theorem f...

It is well known that the variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest and analyze some new proximal point methods for solving the variational inequalities. These new methods include the explicit, the implicit, and the extragradient methods as special cases. The convergence analysis of the new methods is considered...

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

We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild a...

This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another alg...