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

    Khanittha Promluang Info
    Kanokwan Sitthithakerngkiet Info
    Poom Kumam Info

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 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

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January 26, 2016
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2016-01-26

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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

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