ITERATIVE METHODS FOR APPROXIMATION OF FIXED POINTS AND THEIR APPLICATIONS
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- Takahashi Wataru
- Tokyo Institute of Technology
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Abstract
In this article, we deal with iterative methods for approximation of fixed points and their applications, We first discuss fixed point theorems for a nonexpansive mapping or a family of nonexpansive mappings. In particular, we state a fixed point theorem which answered affirmatively a problem posed during the Conference on Fixed Point Theory and Applications held at CIRM, Marseille-Luminy, 1989. Then we discuss nonlinear ergodic theorems of Baillon's type for nonlinear semigroups of nonexpansive mappings. In particular, we state nonlinear ergodic theorems which answered affirmatively the problem posed during the Second World Congress on Nonlinear Analysts, Athens, Greece, 1996. Next, we deal with weak and strong convergence theorems of Mann's type and Halpern's type in a Banach space. Finally, using these results, we consider the feasibility problem by convex combinations of nonexpansive retractions and the convex minimization problem of finding a minimizer of a convex function.
Journal
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- Journal of the Operations Research Society of Japan
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Journal of the Operations Research Society of Japan 43 (1), 87-108, 2000
The Operations Research Society of Japan
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Details 詳細情報について
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- CRID
- 1390282679086140544
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- NII Article ID
- 110001183904
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- NII Book ID
- AA00703935
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- ISSN
- 21888299
- 04534514
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- NDL BIB ID
- 5316473
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed