Kohsaka, Fumiaki; Takahashi, Wataru Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces. (English) Zbl 1149.47045 Arch. Math. 91, No. 2, 166-177 (2008). 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. Reviewer: Vasile Berinde (Baia Mare) Cited in 5 ReviewsCited in 144 Documents MSC: 47H10 Fixed-point theorems 47H05 Monotone operators and generalizations Keywords:Banach space; firmly nonexpansive mapping; nonspreading mapping; resolvent; monotone operator; fixed point; commutative family PDF BibTeX XML Cite \textit{F. Kohsaka} and \textit{W. Takahashi}, Arch. Math. 91, No. 2, 166--177 (2008; Zbl 1149.47045) Full Text: DOI OpenURL