Journal
ARCHIV DER MATHEMATIK
Volume 91, Issue 2, Pages 166-177Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00013-008-2545-8
Keywords
firmly nonexpansive mapping; firmly nonexpansive type mapping; fixed point theorem; nonspreading mapping; resolvent of monotone operator
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In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced class of firmly nonexpansive type mappings in Banach spaces and the class of firmly nonexpansive mappings in Hilbert spaces. Among other things, we obtain a fixed point theorem for a single nonspreading mapping in Banach spaces. Using this result, we also obtain a common fixed point theorem for a commutative family of nonspreading mappings in Banach spaces.
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