Taiwanese Journal of Mathematics

Generalized Projection Algorithms for Maximal Monotone Operators and Relatively Nonexpansive Mappings in Banach Spaces

Chakkrid Klineam, Suthep Suantai, and Wataru Takahashi

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Abstract

In this paper, we prove strong convergence theorems of modified Halpern’s iteration for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a relatively nonexpansive mapping in a Banach space by using two hybrid methods. Using these results, we obtain new convergence results for resolvents of maximal monotone operators and relatively nonexpansive mappings in Banach spaces.

Article information

Source
Taiwanese J. Math., Volume 15, Number 3 (2011), 1227-1246.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406296

Digital Object Identifier
doi:10.11650/twjm/1500406296

Mathematical Reviews number (MathSciNet)
MR2829908

Zentralblatt MATH identifier
1256.47051

Subjects
Primary: 47H05: Monotone operators and generalizations 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H17

Keywords
uniformly convex Banach space generalized projection relatively nonexpansive mapping maximal monotone operator fixed point

Citation

Klineam, Chakkrid; Suantai, Suthep; Takahashi, Wataru. Generalized Projection Algorithms for Maximal Monotone Operators and Relatively Nonexpansive Mappings in Banach Spaces. Taiwanese J. Math. 15 (2011), no. 3, 1227--1246. doi:10.11650/twjm/1500406296. https://projecteuclid.org/euclid.twjm/1500406296


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References

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