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1999 Nonlinear ergodic theorems for a semitopological semigroup of non-Lipschitzian mappings without convexity
G. Li, J. K. Kim
Abstr. Appl. Anal. 4(1): 49-59 (1999). DOI: 10.1155/S1085337599000056

Abstract

Let G be a semitopological semigroup, C a nonempty subset of a real Hilbert space H, and ={Tt:tG} a representation of G as asymptotically nonexpansive type mappings of C into itself. Let L(x)={zH:infsGsuptGTtsxz=inftGTtxz} for each xC and L()=xCL(x). In this paper, we prove that sGconv¯{Ttsx:tG}L() is nonempty for each xC if and only if there exists a unique nonexpansive retraction P of C into L() such that PTs=P for all sG and P(x)conv¯{Tsx:sG} for every xC. Moreover, we prove the ergodic convergence theorem for a semitopological semigroup of non-Lipschitzian mappings without convexity.

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G. Li. J. K. Kim. "Nonlinear ergodic theorems for a semitopological semigroup of non-Lipschitzian mappings without convexity." Abstr. Appl. Anal. 4 (1) 49 - 59, 1999. https://doi.org/10.1155/S1085337599000056

Information

Published: 1999
First available in Project Euclid: 9 April 2003

zbMATH: 0988.47039
MathSciNet: MR1799460
Digital Object Identifier: 10.1155/S1085337599000056

Subjects:
Primary: 47H09 , 47H10
Secondary: 47H20

Rights: Copyright © 1999 Hindawi

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