System of Nonlinear Set-Valued Variational Inclusions Involving a Finite Family of H ( · , · ) -Accretive Operatorsin Banach Spaces

Abstract

We study a new system of nonlinear set-valued variational inclusions involving a finite familyof $H(·,·)$-accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite familyof $H(·,·)$-accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variationalinclusions. Moreover, we introduce a new iterative scheme and prove a strong convergence theorem for finding solutions for this system.