Proximal Point Algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis
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.
Keywords:
Proximal Point Algorithm, Zero point, inverse strongly accretive operator, nonexpansive mappingHow to Cite
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Copyright (c) 2016 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2016 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.