Fixed point theorems for nonexpansive mappings on nonconvex sets in uced banach spaces

Wei Shih Dlu; Young Y.E. Huang; Chi Lin Yen

doi:10.1155/S0161171202107113

Fixed point theorems for nonexpansive mappings on nonconvex sets in uced banach spaces

Wei Shih Dlu
, Young Y.E. Huang
, Chi Lin Yen

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

It is shown that every asymptotically regular or λ-firmly nonexpansive mapping T:C→C 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 (T i) iεI is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of T i, iεI, have a nonempty intersection, then T i, iεI, have a common fixed point in C:

Original language	English
Pages (from-to)	251-257
Number of pages	7
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	31
Issue number	4
DOIs	https://doi.org/10.1155/S0161171202107113
Publication status	Published - 2002
Externally published	Yes

ASJC Scopus subject areas

Mathematics (miscellaneous)

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abstract = "It is shown that every asymptotically regular or λ-firmly nonexpansive mapping T:C→C 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 (T i) iεI is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of T i, iεI, have a nonempty intersection, then T i, iεI, have a common fixed point in C:",

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year = "2002",

doi = "10.1155/S0161171202107113",

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pages = "251--257",

journal = "International Journal of Mathematics and Mathematical Sciences",

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AU - Dlu, Wei Shih

AU - Huang, Young Y.E.

AU - Yen, Chi Lin

PY - 2002

Y1 - 2002

N2 - It is shown that every asymptotically regular or λ-firmly nonexpansive mapping T:C→C 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 (T i) iεI is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of T i, iεI, have a nonempty intersection, then T i, iεI, have a common fixed point in C:

AB - It is shown that every asymptotically regular or λ-firmly nonexpansive mapping T:C→C 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 (T i) iεI is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of T i, iεI, have a nonempty intersection, then T i, iεI, have a common fixed point in C:

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UR - https://www.scopus.com/pages/publications/17844368089#tab=citedBy

U2 - 10.1155/S0161171202107113

DO - 10.1155/S0161171202107113

M3 - Article

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JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

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ER -

Fixed point theorems for nonexpansive mappings on nonconvex sets in uced banach spaces

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