Danes' Drop Theorem in locally convex spaces

Authors:
Cheng Lixin, Zhou Yunchi and Zhang Fong

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3699-3702

MSC (1991):
Primary 46A22

DOI:
https://doi.org/10.1090/S0002-9939-96-03404-1

MathSciNet review:
1328359

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Danes' Drop Theorem is generalized to locally convex spaces.

**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**

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:
https://doi.org/10.1090/S0002-9939-96-03404-1

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

Article copyright:
© Copyright 1996
American Mathematical Society