H-Mixed Accretive Mapping and Proximal Point Method for Solving a System of Generalized Set-Valued Variational Inclusions. (11th June 2021)

• Record Type: Journal Article
• Authors: Bhat, Mohd Iqbal; Shafi, Sumeera; Malik, Mudasir Ahmad
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 8(2021)
• Page Start: 955
• Page End: 972
• Publication Date: 2021-06-11
• Subjects: Convergence analysis -- iterative algorithm -- mixed accretive mapping -- proximal-point mapping -- q-uniformly smooth Banach spaces -- system of generalized set-valued variational inclusion problems; 47H09 -- 47J20 -- 49J40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1933527
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we introduce a new system of variational inclusion problems called system of generalized set-valued variational inclusion problems involving α β - H ( ( ., . ), ( ., . ) ) -mixed accretive mapping in q -uniformly smooth Banach spaces. By means of proximal-point mapping method, we prove the existence of solution of this system of variational inclusions. Further, we propose an iterative algorithm for finding the approximate solution of the system. Furthermore, we prove that the sequences generated by the iterative algorithm converge strongly to a solution of the system.