Approximate Rolle’s theorems for the proximal subgradient and the generalized gradient
| dc.contributor.author | Azagra Rueda, Daniel | |
| dc.contributor.author | Ferrera Cuesta, Juan | |
| dc.contributor.author | López-Mesas Colomina, Fernando | |
| dc.date.accessioned | 2023-06-20T09:31:12Z | |
| dc.date.available | 2023-06-20T09:31:12Z | |
| dc.date.issued | 2003-07-01 | |
| dc.description.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). | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Marie Curie Fellowship of the European Community Training and Mobility of Researches Programme | |
| dc.description.sponsorship | BFM | |
| dc.description.sponsorship | Consejeria de Educación de Madrid | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14501 | |
| dc.identifier.doi | 10.1016/S0022-247X(03)00267-1 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/journal/0022247X | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49793 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of Mathematical Analysis and Applications | |
| dc.language.iso | eng | |
| dc.page.final | 191 | |
| dc.page.initial | 180 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | HPMF-CT-2001-01175 | |
| dc.relation.projectID | 2000/0609 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Rolle theorem | |
| dc.subject.keyword | Proximinal subspace | |
| dc.subject.keyword | Generalized gradient | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Approximate Rolle’s theorems for the proximal subgradient and the generalized gradient | |
| dc.type | journal article | |
| dc.volume.number | 283 | |
| dcterms.references | [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. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 6696556b-dc2e-4272-8f5f-fa6a7a2f5344 | |
| relation.isAuthorOfPublication | 1a91d6af-aaeb-4a3e-90ce-4abdf2b90ac3 | |
| relation.isAuthorOfPublication | 47cb9ee0-975c-4533-a7a4-bc341c8ac1d6 | |
| relation.isAuthorOfPublication.latestForDiscovery | 6696556b-dc2e-4272-8f5f-fa6a7a2f5344 |
Download
Original bundle
1 - 1 of 1
