Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-08T01:24:22.124Z Has data issue: false hasContentIssue false

An Lp inequality

Published online by Cambridge University Press:  14 November 2011

J. R. L. Webb
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, U.K.
Weiyu Zhao
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, U.K.

Synopsis

We obtain an inequality for Lp spaces (1<p >2) which corrects an inequality claimed by Xu and Xu [6] and has connections with some quantities of interest in fixed point theory.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Beauzamy, B.. Introduction to Banach spaces and their geometry, 2nd edn (Amsterdam: North-Holland, 1985).Google Scholar
2Casini, E. and Maluta, E.. Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure. Nonlinear Anal. 9 (1985), 103108.Google Scholar
3Kirk, W. A.. A fixed point theorem for mappings which do not increase distances. Amer. Math. Monthly 72 (1965), 10041006.Google Scholar
4Krasnosel'skii, M. A. and Zabreiko, P. P.. Geometrical methods of nonlinear analysis (Berlin: Springer, 1984).Google Scholar
5Webb, J. R. L. and Zhao, W.. On connections between set and ball measures of noncompactness. Bull. London Math. Soc. (to appear).Google Scholar
6Xu, H. and Xu, Z.. An Lp inequality and its applications to fixed point theory and approximation theory. Proc. Roy. Soc. Edinburgh Sect. A 112 (1989), 343351.CrossRefGoogle Scholar