Fixed point theorems for nonexpansive mappings on nonconvex sets in UCED Banach spaces

It is shown that every asymptotically regular or -firmly nonexpansive mapping T:CC has a fixed point whenever C is a finite union of nonempty weakly compact convex subsets of a Banach space X which is uniformly convex in every direction. Furthermore, if {Ti}iI is any compatible family of strongly no...

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Bibliographic Details
Published inInternational journal of mathematics and mathematical sciences Vol. 31; no. 4; pp. 251 - 257
Main Authors Du, Wei-Shih, Huang, Young-Ye, Yen, Chi-Lin
Format Journal Article
LanguageEnglish
Published Wiley 01.01.2002
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Summary:It is shown that every asymptotically regular or -firmly nonexpansive mapping T:CC has a fixed point whenever C is a finite union of nonempty weakly compact convex subsets of a Banach space X which is uniformly convex in every direction. Furthermore, if {Ti}iI is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of Ti, i I, have a nonempty intersection, then Ti, iI, have a common fixed point in C.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0161-1712
1687-0425
DOI:10.1155/S0161171202107113