WEAK AND STRONG CONVERGENCE THEOREMS FOR POSITIVELY HOMOGENEOUS 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...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 15; no. 3; pp. 961 - 980
Main Authors Takahashi, Wataru, Yao, Jen-Chih
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2011
Subjects
Banach space
Mathematical theorems
Perceptron convergence procedure
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ISSN1027-5487
2224-6851
DOI10.11650/twjm/1500406277

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Summary: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. 2000Mathematics Subject Classification: 47H05, 47H09, 47H20. Key words and phrases: Banach space, Nonexpansive mapping, Fixed point, Generalized nonexpansive mapping, Hybrid method, Mann's iteration.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406277