Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 15, Number 3 (2011), 961-980.
Weak and Strong Convergence Theorems for Positively Homogenuous Nonexpansive Mappings in Banach Spaces
Our purpose in this paper is first to prove a weak convergence theorem by Mann's iteration for positively homogeneous nonexpansive mappings in a Banach space. Further, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove a strong convergence theorem for such mappings. From two results, we obtain weak and strong convergence theorems for linear contractive mappings in a Banach space. These results are new even if the mappings are linear and contractive.
Taiwanese J. Math., Volume 15, Number 3 (2011), 961-980.
First available in Project Euclid: 18 July 2017
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47H05: Monotone operators and generalizations 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]
Takahashi, Wataru; Yao, Jen-Chih. Weak and Strong Convergence Theorems for Positively Homogenuous Nonexpansive Mappings in Banach Spaces. Taiwanese J. Math. 15 (2011), no. 3, 961--980. doi:10.11650/twjm/1500406277. https://projecteuclid.org/euclid.twjm/1500406277