Abstract
This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving H(center dot,center dot)-compression XOR-alpha(M)-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with H(center dot,center dot)-compression XOR-alpha(M)-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a circle plus operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example.