Split monotone variational inclusion problem involving Cayley operators

Abstract

In this article, we introduce a new kind of split monotone variational inclusion problem involving Cayley operator in the setting of infinite-dimensional Hilbert spaces. We develop a general iterative method to approximate the solution of the split monotone variational inclusion problem involving Cayley operator. Under some suitable conditions, a convergence theorem for the sequences generated by the proposed iterative scheme is established, which also solves certain variational inequality problems related to strongly positive linear operators. Finally, a numerical example is presented to study the efficiency of the proposed algorithm through MATLAB programming.

Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems

“…In particular, the variational inclusion theory is a natural development of the variational principle. A variety of approaches have been proposed for solving variational inclusion (2), see [19][20][21][22][23][24][25]. A valuable approach to solve (2) is the well-known forward-backward algorithm ( [26]) defined by…”