Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces. (English) Zbl 1215.65104

Nilsrakoo, Weerayuth; Saejung, Satit

Appl. Math. Comput. 217, No. 14, 6577-6586 (2011).

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.

Reviewer: Jiří Vaníček (Praha)

MSC:

65J15	Numerical solutions to equations with nonlinear operators
46B20	Geometry and structure of normed linear spaces

Keywords:

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

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