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Zbl 1149.47045
Kohsaka, Fumiaki; Takahashi, Wataru
Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces. (English)
[J] Arch. Math. 91, No. 2, 166-177 (2008). ISSN 0003-889X; ISSN 1420-8938/e

The authors introduce the concept of a nonspreading mapping and show that every firmly nonexpansive type mapping is nonspreading. It is also shown that the class of firmly nonexpansive type mappings coincides with that of resolvents of monotone operators in Banach spaces. Fixed point theorems for single nonspreading mapping as well as for a commutative family of nonspreading mappings in Banach spaces are the main results of the paper.
[Vasile Berinde (Baia Mare)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H05 Monotone operators (with respect to duality)

Keywords: Banach space; firmly nonexpansive mapping; nonspreading mapping; resolvent; monotone operator; fixed point; commutative family

Cited in: Zbl 1201.47053

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