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Zbl 1215.65104
Nilsrakoo, Weerayuth; Saejung, Satit
Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces. (English)
[J] Appl. Math. Comput. 217, No. 14, 6577-6586 (2011). ISSN 0096-3003

Authors' abstract: We modify Halpern and Mann's iterations for finding a fixed point of a relatively nonexpansive mapping in a Banach space. Consequently, a strong convergence theorem for a nonspreading mapping is deduced. Using a concept of duality theorems, we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings. Finally, we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space.
[Jiří Vaníček (Praha)]

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
46B20 Geometry and structure of normed spaces

Keywords: relatively quasi-nonexpansive mapping; relatively nonexpansive mapping; generalized nonexpansive mapping; generalized nonexpansive type mapping; maximal monotone operator

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