Proximal Point Algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis
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Publication Details
Author list: Promluang K., Sitthithakerngkiet K., Kumam P.
Publisher: Vilnius Gediminas Technical University Press
Publication year: 2016
Journal: Mathematical Modelling & Analysis (1392-6292)
Volume number: 21
Issue number: 1
Start page: 95
End page: 118
Number of pages: 24
ISSN: 1392-6292
eISSN: 1648-3510
Languages: English-Great Britain (EN-GB)
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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. © 2016, © Vilnius Gediminas Technical University, 2016.
Keywords
inverse strongly accretive operator, Zero point
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