System of nonlinear variational inclusion problems with $(A,\eta)$-maximal monotonicity in Banach spaces

Abstract

This paper deals with a new system of nonlinear variational inclusion problems involving (A, η)-maximal relaxed monotone and relative (A, η)-maximal monotone mappings in 2-uniformly smooth Banach spaces. Using the generalized resolvent operator technique, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also proved for other system of variational inclusion problems involving relative (A, η)-maximal monotone mappings and (H, η)-maximal monotone mappings.

An itertive algorithm with error terms for solving a system of implicit n-variational inclusions

“…Iterative algorithms have been used by different researchers to solve different classes of variational inequalities and variational inclusion problems. For further information one can see [6,8,9,10,11,12,13,14,15,19,20,21,24,25,26,28] and references therein. A new problem of much more interest which is called as system of variational inequalities (inclusions) were introduced and studied in the literature.…”