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...

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...

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...

We propose a modified extragradient method for solving the variational inequality problem in Hilbert space. The is combination of well-known subgradient with Mann’s mean value which updated iterate picked convex hull all previous iterates. show weak convergence to solution problem, provided that condition on corresponding averaging matrix fulfilled. Some numerical experiments are given effectiv...

In this paper, we suggest a hybrid extragradient method for finding a common element of the set of fixed point sets of an infinite family of nonexpansive mappings and the solution set of the split feasibility problem (SFP) in real Hilbert spaces.

We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like a...

This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong convergence of an algorithm can be verified in the infinite-dimensional Hilbert spaces. Moreover, several numerical results are given to show the effectiveness of our algorithm.