Publication:
Approximate Rolle’s theorems for the proximal subgradient and the generalized gradient

Thumbnail Image
Files
2003approximaterolle2.pdf (4.28 MB)
Official URL
http://www.sciencedirect.com/science/journal/0022247X
Full text at PDC
Publication Date
2003-07-01
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Citations
Google Scholar
Exportar
DC QDC MarcXML RDF MODS METS ORE-ATOM
Research Projects
Organizational Units
Journal Issue
Abstract
We establish approximate Rolle's theorems for the proximal subgradient and for the generalized gradient. We also show that an exact Rolle's theorem for the generalized gradient is completely false in all infinite-dimensional Banach spaces (even when they do not possess smooth bump functions).
Description
UCM subjects
Análisis matemático
Unesco subjects
1202 Análisis y Análisis Funcional
Keywords
Citation
[1] D. Azagra, Smooth negligibility and subdifferential ca1culus in Banach spaces, with applications, Ph.D. dissertation, Universidad Complutense de Madrid, October 1997. [2] D. Azagra, R. Deville, Subdifferential Rolle's and mean value inequality theorems, Bull. Austral. Math. Soc. 56 (1997) 319-329. [3] D. Azagra, J. Gómez, J.A. Jaramillo, Rolle's theorem and negligibility of points in infinite-dimensional Banach spaces, J. Math. Anal. Appl. 213 (1997) 487--495. [4] D. Azagra, M. Jiménez-Sevilla, The failure of Rolle's theorem in infinite-dimensiOl1al Banach spaces, J. Funct. Anal. 182 (2001) 207-226. [5] J. Bes, J. Ferrera, On a multidimensional version of Rolle's theorem, Publ. Dto. Análisis Mat. UCM 1 (1996/1997) 21-27. [6] F.H. Clark, Yu.S. Ledyaev, R.J. Stem, P.R. Wolensk.i, Nonsmooth Analysis and Control Theory, in: Graduate Texts in Mathematics, Vol. 178, Springer, 1998. [7] R. Deville, A mean value theorem for nondifferentiable mappings in Banach spaces, Serdica Math. J. 21 (1995) 59-66. [8] R. Deville, G. Godefroy, V. Zizler, Smoothness and Renorrnings in Banam Spaces, in: Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 64, 1993. [9] 1. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. (N.S.) 1 (1979) 443-474. [10] 1. Ferrer, Rolle's, theorem fail in [2, Amer. Math. Monthly 103 (1996) 161-165. [11] G. Godefroy, Sorne remarks on subdifferential calculus, Rev. Mat. Complut. 11 (1998) 269-279. [12] S.A. Shkarin, On Rolle's theorem in infinite-dimensional Banach espaces, transl. from Mat. Zametki 51 (1992) 128-136.
URI
https://hdl.handle.net/20.500.14352/49793
Collections
Artículos