On a fixed point theorem of Greguš

Brian Fisher and Salvatore Sessa

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-6

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. ‖ T I x − I T x ‖ ≤ ‖ I x − T x ‖ for any x in X , and satisfy the inequality ‖ T x − T y ‖ ≤ a ‖ I x − I y ‖ + ( 1 − a ) max { ‖ T x − I x ‖ , ‖ T y − I y ‖ } 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 I C contains T C , then T and I have a unique common fixed point in C .

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:191262

DOI: 10.1155/S0161171286000030

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