Error Estimate of Data Dependence for Discontinuous Operators by New Iteration Process with Convergence Analysis. (26th October 2019)

• Record Type: Journal Article
• Authors: Kumam, Wiyada; Khammahawong, Konrawut; Kumam, Poom
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 14(2019)
• Page Start: 1644
• Page End: 1677
• Publication Date: 2019-10-26
• Subjects: Collage theorem -- data dependency -- discontinuous operators -- inverse problem -- iterative scheme -- strong convergence; 65J15 -- 65J22 -- 47H10 -- 47N40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1610437
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we introduce a new discontinuous operator and investigate the existence and uniqueness of fixed points for the operators in complete metric spaces. We also provide rate of convergence and data dependency of S-iterative scheme for a fixed point of the discontinuous operators in Banach spaces. Moreover, we prove the estimation Collage theorems and compare error estimate between data dependency and Collage theorems. Numerical examples are provided to support our results.