Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-24T00:09:33.194Z Has data issue: false hasContentIssue false
  • English
  • Français

An Lp inequality and its applications to fixed point theory and approximation theory

Published online by Cambridge University Press:  14 November 2011

Hong-Kun Xu  and
Zong-Ben Xu
Hong-Kun Xu
Affiliation:
Department of Mathematics, Xi'an Jiaotong University, Xi'an, The People's Republic of China
Zong-Ben Xu
Affiliation:
Department of Mathematics, Xi'an Jiaotong University, Xi'an, The People's Republic of China
Get access Rights & Permissions [Opens in a new window]

Synopsis

An Lp inequality for l < p < 2 is established and applications to fixed points of uniformly Lipschitz mappings and strongly unique best approximations are given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 343 - 351
Copyright
Copyright © Royal Society of Edinburgh 1989

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

1Amir, D.. On Jung's constant and related constants in normed linear spaces. Pacific J. Math. 118 (1985), 1–15.CrossRefGoogle Scholar
2Beauzamy, B.. Introduction to Banach Spaces and Their Geometry, 2nd edn (Amsterdam: North-Holland, 1985).Google Scholar
3Bynum, W. L.. Normal structure coefficients for Banach spaces. Pacific J. Math. 86 (1980), 427–436.Google Scholar
4Casini, E. and Maluta, E.. Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure. Nonlinear Anal. 9 (1985), 103–108.Google Scholar
5Goebel, K. and Kirk, W. A.. A fixed point theorem for transformations whose iterates have uniform Lipschitz constant. Studia Math. 47 (1973), 130–135.Google Scholar
6Lifschitz, E. A.. Fixed point theorems for operators in strongly convex spaces. Voronez Gos. Univ. Trudy Math. Fak. 16 (1975), 23–28.Google Scholar
7Lim, T. C.. Fixed point theorems for uniformly Lipschitzian mappings in L p spaces. Nonlinear Anal. 7 (1983), 555–563.CrossRefGoogle Scholar
8Lim, T. C.. On the normal structure coefficient and the bounded sequence coefficient. Proc. Amer. Math. Soc. 88 (1983), 262–264.Google Scholar
9Lim, T. C.. Some L p inequalities and their applications to fixed point theorems of uniformly Lipschitzian mappings. Proc. Sympos. Pure Math. 45 (1986), pt. 2, 119–125.Google Scholar
10Maluta, E.. Uniformly normal structure and related coefficients. Pacific J. Math. 111 (1984), 357–369.Google Scholar
11Prus, B. and Smarzewski, R.. Strongly unique best approximations and centers in uniformly convex spaces. J. Math. Anal. Appl. 111 (1987), 10–21.CrossRefGoogle Scholar
12Smarzewski, R.. Strongly unique best approximation in Banach spaces. J. Approx. Theory 47 (1986), 184–194.CrossRefGoogle Scholar