Convergence analysis and stability of perturbed three-step iterative algorithm for generalized mixed ordered quasi-variational inclusion involving XOR operator. (2nd April 2020)

• Record Type: Journal Article
• Authors: Ahmad, Iqbal; Rahaman, Mijanur; Ahmad, Rais; Ali, Imran
• Is Part Of: Optimization. Volume 69:Number 4(2020)
• Page Start: 821
• Page End: 845
• Publication Date: 2020-04-02
• Subjects: Convergence -- quasi-variational inclusion -- stability -- algorithm -- XOR operator; 47H09 -- 49J40; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1652910
• Languages: English
• ISSNs: 0233-1934

Abstract

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.