Stability analysis for generalized nonlinear mixed ordered implicit quasi-variational inclusion problem involving ⊕ operation

Abstract

In this article, we introduce a generalized nonlinear mixed ordered implicit quasi-variational inclusion problem involving ⊕ operation in the setting of real ordered positive Hilbert spaces. We propose a perturbed three-step iterative algorithm for solving generalized nonlinear mixed ordered implicit quasi-variational inclusion problem involving ⊕ operator. By using a new resolvent operator method with XOR technique, we prove the existence of solution of generalized nonlinear mixed ordered implicit quasi-variational inclusion problem involving ⊕ operator and discuss the convergence analysis as well as stability analysis 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 construct a numerical example and a convergence graph in support of our main result by using MATLAB programming.