A note on Picard iterates of nonexpansive mappings

• Autorzy: Eun Suk Kim , W. A. Kirk
• Języki publikacji: EN

Abstrakty

EN

Let X be a Banach space, C a closed subset of X, and T:C → C a nonexpansive mapping. It has recently been shown that if X is reflexive and locally uniformly convex and if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). In this paper it is shown that if T is assumed to be asymptotically regular, this condition can be weakened much further. Finally, some observations are made about the geometric conditions imposed.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 47H10: Fixed-point theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2001
• Tom: 76
• Numer: 3
• Strony: 189-196

Daty

wydano

2001

Twórcy

autor

Eun Suk Kim

• Department of Applied Mathematics, Pukyong National University, Pusan 608-737, South Korea

autor

W. A. Kirk

• Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, U.S.A.

Identyfikatory

DOI

10.4064/ap76-3-2