Proximal Point Algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Promluang, Khanittha; Sitthithakerngkiet, Kanokwan; Kumam, Poom
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 1(2016)
• Page Start: 95
• Page End: 118
• Publication Date: 2016-01-02
• Subjects: Proximal Point Algorithm -- Zero point -- inverse strongly accretive operator -- nonexpansive mapping; 47H10 -- 47H09; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1137090
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: In this paper, we investigate and analyze a proximal point algorithm via viscosity approximation method with error. This algorithm is introduced for finding a common zero point for a countable family of inverse strongly accretive operators and a countable family of nonexpansive mappings in Banach spaces. Our result can be extended to some well known results from a Hilbert space to a uniformly convex and 2 − uniformly smooth Banach space. Finally, we establish the strong convergence theorems for the proximal point algorithm. Also, some illustrative numerical examples are presented.