Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces. (English) Zbl 1149.47045

Kohsaka, Fumiaki; Takahashi, Wataru

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)

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