Topological Methods in Nonlinear Analysis

Nonlinear submeans on semigroups

Anthony To-Ming Lau and Wataru Takahashi

Full-text: Open access

Abstract

The purpose of this paper is to study some algebraic structure of submeans on certain spaces $X$ of bounded real valued functions on a semigroup and to find local conditions on $X$ in terms of submean for the existence of a left invariant mean.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 22, Number 2 (2003), 345-353.

Dates
First available in Project Euclid: 30 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1475266341

Mathematical Reviews number (MathSciNet)
MR2036381

Zentralblatt MATH identifier
1039.43002

Citation

Lau, Anthony To-Ming; Takahashi, Wataru. Nonlinear submeans on semigroups. Topol. Methods Nonlinear Anal. 22 (2003), no. 2, 345--353. https://projecteuclid.org/euclid.tmna/1475266341


Export citation

References

  • M. Despic and F. Ghahramani, Weak amenability of group algebras of locally comact groups , Canad. Math. Bull., 37 (1994), 165–167
  • \ref\key 2R. Ellis, Locally compact transformation groups , Duke Math. J., 24 (1957), 119–125 \ref\key 3
  • Ky Fan, Existence theorems and extreme solutions for inequalities concerning convex functions or linear transformations , Math. Z., 68 (1957), 205–217 \ref\key 4
  • E. E. Granirer and A. T. Lau, Invariant means on locally compact groups , Illinois J. Math. 15 (1971), 249–257 \ref\key 5
  • B. Johnson, Weak amenability of group algebras , Bull. London Math. Soc. 23 (1991), 281–284 \ref\key 6
  • A. T. Lau and W. Takahashi, Invariant means and fixed point properties for non-expansive representations of topological semigroups , Topol. Methods Nonlinear Anal., 5 (1995), 39–57 \ref\key 7 ––––, Invariant submeans and semigroups of nonexpansive mappings in Banach spaces with normal structures , J. Funct. Anal., 25 (1996), 79–88 \ref\key 8
  • N. Mizoguchi and W.Takahashi, On the existence of fixed points and ergodic retractions for Lipshitzian semigroups in Hilbert spaces , Nonlinear Anal., 14 (1990), 69–80 \ref\key 9
  • W. Ruppert, Rechstopologische Halbgruppen , J. Angew. Math., 261 (1973), 123–133 \ref\key 10
  • K. Sakamaki and W. Takahashi, Systems of convex inequalities and their applications , J. Math. Anal. Appl. 70 (1979), 445–459 \ref\key 11
  • W. Takahashi, Fixed point theorem and nonlinear ergodic theorem for nonexpansive semigroups without convexity , Canad. J. Math., 44(1992), 880–887 \ref\key 12
  • W. Takahashi and D. H. Jeong, Fixed Point theorem for nonexpansive semigroups on Banach space , Proc. Amer. Math. Soc., 122(1994), 1175–1179 \ref\key 13
  • J. C. S. Wong, Topologically stationary locally compact groups and amenability, Trans. Amer. Math. Soc., 144 (1969), 351–363