Research Article A General Projection Method for a System of Relaxed Cocoercive Variational Inequalities in Hilbert Spaces
نویسندگان
چکیده
Recommended by Saburou Saitoh We consider a new algorithm for a generalized system for relaxed cocoercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods. Our results include the previous results as special cases extend and improve the main results of R.
منابع مشابه
General Projection Systems and Relaxed Cocoercive Nonlinear Variational Inequalities
We explore the solvability of a general system of nonlinear relaxed cocoercive variational inequality (SNVI) problems based on a new projection system for the direct product of two nonempty closed and convex subsets of real Hilbert spaces. 2000 Mathematics subject classification: primary 49J40, 65B05; secondary 47H20.
متن کاملProjection Type Method for Generalized System of Relaxed Cocoercive Variational Inequalities in Hilbert Spaces
The approximate solvability of a system of nonlinear variational inequalities involving two relaxed cocoercive mappings in Hilbert spaces is considered by exploiting projection methods. The results presented in this paper extend and improve the main results of Chang et al. [1], Verma [2, 3 ,4], Xiu and Zhang [5] and Nie et al. [6].
متن کاملA New System of Generalized Nonlinear Relaxed Cocoercive Variational Inequalities
We introduce and study a new system of generalized nonlinear relaxed cocoercive inequality problems and construct an iterative algorithm for approximating the solutions of the system of generalized relaxed cocoercive variational inequalities in Hilbert spaces. We prove the existence of the solutions for the system of generalized relaxed cocoercive variational inequality problems and the converg...
متن کاملComments on relaxed $(gamma, r)$-cocoercive mappings
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...
متن کاملA Resolvent Operator Technique for Solving Generalized System of Nonlinear Relaxed Cocoercive Mixed Variational Inequalities
The aim of this work is to use resolvent operator technique to find the common solutions for a system of generalized nonlinear relaxed cocoercive mixed variational inequalities and fixed point problems for Lipschitz mappings in Hilbert spaces. The results obtained in this work may be viewed as an extension, refinement and improvement of the previously known results.
متن کامل