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Title: On a fixed point theorem of Greguš
Authors: Fisher, Brian
Sessa, S.
First Published: 1986
Publisher: Hindawi Publishing Corporation
Citation: International Journal of Mathematics and Mathematical Sciences Volume 9 (1986), Issue 1, Pages 23-28
Abstract: We consider two selfmaps T and I of a closed convex subset C of a Banach space X which are weakly commuting in X, i.e. ‖TIx−ITx‖≤‖Ix−Tx‖   for   any   x   in   X, and satisfy the inequality ‖Tx−Ty‖≤a‖Ix−Iy‖+(1−a)max{‖Tx−Ix‖,‖Ty−Iy‖} for all x, y in C, where 0<a<1. It is proved that if I is linear and non-expansive in C and such that IC contains TC, then T and I have a unique common fixed point in C.
DOI Link: 10.1155/S0161171286000030
ISSN: 0161-1712
eISSN: 1687-0425
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Appears in Collections:Published Articles, Dept. of Mathematics

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