Convergence analysis and stability of perturbed three-step iterative algorithm for generalized mixed ordered quasi-variational inclusion involving XOR operator

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.

KEYWORDS:

• Convergence
• quasi-variational inclusion
• stability
• algorithm
• XOR operator

MSC:

• 47H09
• 49J40

Disclosure statement

No potential conflict of interest was reported by the authors.