Abstract In this paper, a simple proof of the convergence recent iterative algorithm by relaxed $(u, v)$ ( u , v ) -cocoercive mappings due to Imnang (J. Inequal. Appl. 2013:249, 2013) is presented.

Variational inequality methods whether based on numerous available new algorithms or otherwise have been applied vigorously, especially to model equilibria problems in economics, optimization and control theory, operations research, transportation network modeling, and mathematical programming, while a considerable progress to developing general methods for the sensitivity analysis for variatio...

The main contributions of this paper is twofold. First, our primary concern to suggest a new iterative algorithm using the P-?-proximal-point mapping technique and Nadler?s for finding approximate solutions system generalized multi-valued nonlinear variational-like inclusions. Under some appropriate conditions imposed on parameters mappings involved in inclusions, strong convergence sequences g...

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudoco...

The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let K1 and K2 be nonempty closed convex subsets o...

we show that the variational inequality $vi(c,a)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-lipschitzian mapping $a: cto h$ with $r>gamma mu^2$, where$c$ is a nonempty closed convex subset of a hilbert space $h$. fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...

This paper is concerned with a common element of the set of common fixed points for two infinite families of strictly pseudocontractive mappings and the set of solutions of a system of cocoercive quasivariational inclusions problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a novel general iterative scheme based on the viscosity approximation method...

We show that the variational inequality $VI(C,A)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-Lipschitzian mapping $A: Cto H$ with $r>gamma mu^2$, where$C$ is a nonempty closed convex subset of a Hilbert space $H$. Fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...

We introduce a new iterative scheme by modifying Mann’s iteration method to find a common element for the set of common fixed points of an infinite family of asymptotically strictly pseudocontractive mappings in the intermediate sense, the set of solutions of the cocoercive quasivariational inclusions problems, and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The st...

*Correspondence: [email protected] 3Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran Full list of author information is available at the end of the article Abstract In this paper, we introduce and consider a new system of generalized nonlinear mixed variational inequalities involving six different nonlinear operators and discuss the existence and uniqueness of s...