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Proximal Point Algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis

    Khanittha Promluang Affiliation
    ; Kanokwan Sitthithakerngkiet Affiliation
    ; Poom Kumam Affiliation

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.

Keyword : Proximal Point Algorithm, Zero point, inverse strongly accretive operator, nonexpansive mapping

How to Cite
Promluang, K., Sitthithakerngkiet, K., & Kumam, P. (2016). Proximal Point Algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis. Mathematical Modelling and Analysis, 21(1), 95-118. https://doi.org/10.3846/13926292.2016.1137090
Published in Issue
Jan 26, 2016
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