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Promluang, Khanittha; Sitthithakerngkiet, Kanokwan; Kumam, Poom

Proximal point algorithm for a common of countable families of inverse strongly accretive operators and nonexpansive mappings with convergence analysis. (English) Zbl 1483.47101

Math. Model. Anal. 21, No. 1, 95-118 (2016).
Summary: 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 strong convergence theorems for the proximal point algorithm. Also, some illustrative numerical examples are presented.

Cited in 1 Document

MSC:

47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

proximal point algorithm; zero point; inverse strongly accretive operator; nonexpansive mapping; strong convergence
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References:

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