|
Danes' Drop Theorem in locally convex spaces
Author(s):
Cheng
Lixin;
Zhou
Yunchi;
Zhang
Fong
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3699-3702.
MSC (1991):
Primary 46A22
MathSciNet review:
1328359
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Danes' Drop Theorem is generalized to locally convex spaces.
References:
- 1.
- J. Danes, A geometric theorem useful in nonlinear functional analysis, Boll. Un. Mat. Ital. 6 (1972), 369-372. MR 47:5678
- 2.
- -, Equivalence of some geometric and related results of nonlinear functional analysis, Comment. Math. Univ. Carolinae 26 (1985), 443-454. MR 88a:47053
- 3.
- S. Rolewicz, On drop property, Studia Math. 85 (1986), 27-35. MR 88g:46033
- 4.
- J. R. Giles and Denka N. Kutzarova, Characterization of drop and weak drop properties for closed bounded convex sets, Bull. Austral. Math. Soc. 43 (1991), 377-385. MR 92d:46036
- 5.
- H. Brezis and F. E. Browder, A general principle on ordered sets in nonlinear functional analysis, Adv. in Math. 21 (1976), 355-364. MR 54:13641
- 6.
- F. Browder, Normal solvability and the Fredholm alternative for mappings into infinite dimensional manifolds, J. Funct. Anal. 8 (1971), 250-274. MR 44:5834
- 7.
- M. M. Day, Normed linear spaces, Springer, 1973. MR 49:9588
- 8.
- S. Dolecki and J. P. Penot, The Clark's tangent cone and limits of tangent cones, Publ. Math. Pau (1983), II-1-11.
- 9.
- M. Turcini, Mapping theorems via variable drops in Banach spaces, Rend. Istit. Lombardo, Sci. A 114 (1980), 164-168.
- 10.
- J. R. Giles, Brailey Sims and A. C. Yorke, On the drop and weak drop properties for a Banach spaces, Bull. Austral. Math. Soc. 41 (1990), 503-507. MR 91i:46014
- 11.
- Denka N. Kutzarova, On drop property of convex sets in Banach spaces, Constructive Theory of Functions' 87, Sofia (1988), 283-287.
- 12.
- D. N. Kutzarova and S. Rolewicz, On drop property for convex sets, Arch. Math. (Basel) 57 (1991), 385-394. MR 92i:46020
- 13.
- R. R. Phelps, Convex functions, monotone operators and differentiability, Lecture Notes in Math., vol. 1364, Springer-Verlag, 1989. MR 90g:46063
- 14.
- J. R. Giles, Convex analysis with application in the differentiation of convex functions, Pitman Res. Notes in Math., vol. 58, 1982. MR 83g:46001
- 15.
- P. Georgiev, D. Kutzarova and A. Maaden, On the smooth drop property, Nonlinear Anal. 26 (1996), 595-602. CMP 96:03
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
46A22
Retrieve articles in all Journals with
MSC (1991):
46A22
Additional Information:
Cheng
Lixin
Affiliation:
Department of Mathematics, Jianghan Petroleum Institute, Hubei 434102, People's Republic of China
Address at time of publication:
Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
Zhou
Yunchi
Affiliation:
Department of Mathematics, Jianghan Petroleum Institute, Hubei 434102, People's Republic of China
Zhang
Fong
Affiliation:
Department of Mathematics, Jianghan Petroleum Institute, Hubei 434102, People's Republic of China
DOI:
10.1090/S0002-9939-96-03404-1
PII:
S 0002-9939(96)03404-1
Keywords:
Locally convex space,
Banach space,
Danes' Drop Theorem,
separated sets
Received by editor(s):
December 12, 1994
Received by editor(s) in revised form:
April 5, 1995
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1996,
American Mathematical Society
|
