Abstract
In this article, we introduce a new type of generalized mixed ordered quasi-variational inclusion problem in the setting of real ordered Hilbert spaces. Further, we propose a perturbed three-step iterative algorithm for solving generalized mixed ordered quasi-variational inclusion problem. By using the relaxed resolvent operator method with XOR technique, we prove the existence of solution of generalized mixed ordered quasi-variational inclusion problem and discuss the convergence analysis and stability of the proposed algorithm. The iterative algorithm and results presented in this paper generalize, improve and significantly refine many previously known results of this area. Moreover, we give a numerical example to illustrate and show the convergence of the proposed algorithm in support of our main result.