Convergence analysis of a three-step iterative algorithm for generalized set-valued mixed-ordered variational inclusion problem

This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving H(·, ·)-compression XOR-α_M-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with H(·, ·)-compression XOR-α_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 ⊕ 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.