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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. [ABSTRACT FROM AUTHOR]

In this paper, we define a generalized resolvent operator involving a 풢 ⁢ (⋅ , ⋅) -co-monotone mapping for solving a generalized variational inclusion problem. We show that the resolvent operator under consideration is single-valued as well as Lipschitz continuous. An iterative algorithm is constructed to obtain the approximate solution of our problem. An example is provided to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]