Taiwanese Journal of Mathematics

Proximal Point Methods for Monotone Operators in Banach Spaces

Koji Aoyama, Fumiaki Kohsaka, and Wataru Takahashi

Full-text: Open access

Abstract

Some fundamental properties of resolvents of monotone operators in Banach spaces are investigated. Using them, we study the asymptotic behavior of the sequences generated by two modifications of the proximal point algorithm for monotone operators satisfying a range condition defined in Banach spaces.

Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 259-281.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406174

Digital Object Identifier
doi:10.11650/twjm/1500406174

Mathematical Reviews number (MathSciNet)
MR2780284

Zentralblatt MATH identifier
1241.47044

Subjects
Primary: 47H05: Monotone operators and generalizations 47J25: Iterative procedures [See also 65J15]

Keywords
convex function firmly nonexpansive-type mapping fixed point minimization monotone operator proximal point algorithm uniformly convex Banach space zero point

Citation

Aoyama, Koji; Kohsaka, Fumiaki; Takahashi, Wataru. Proximal Point Methods for Monotone Operators in Banach Spaces. Taiwanese J. Math. 15 (2011), no. 1, 259--281. doi:10.11650/twjm/1500406174. https://projecteuclid.org/euclid.twjm/1500406174


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