Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving ( A , η ) -Maximal Relaxed Monotone Operators

Abstract

We introduce and study a class of new general systems of set-valued variational inclusions involving $(A,\eta )$-maximal relaxed monotone operators in Hilbert spaces. By using the general resolvent operator technique associated with $(A,\eta )$-maximal relaxed monotone operators, we construct some new iterative algorithms for finding approximation solutions to the general system of set-valued variational inclusion problem and prove the convergence of this algorithm. Our results improve and extend some known results.