caa a22 4500 463206088 CHVBK 20180405153126.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s11228-007-0043-y doi (NATIONALLICENCE)springer-10.1007/s11228-007-0043-y Generalized Jacobian for Functions with Infinite Dimensional Range and Domain [Elektronische Daten] [Zsolt Páles, Vera Zeidan] In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon-Nikodým property, Clarke's generalized Jacobian will be extended to this setting. Characterization and fundamental properties of the extended generalized Jacobian are established including the nonemptiness, the β-compactness, the β-upper semicontinuity, and a mean-value theorem. A connection with known notions is provided and chain rules are proved using key results developed. This included the vectorization and restriction theorem, and the extension theorem. Therefore, the generalized Jacobian introduced in this paper is proved to enjoy all the properties required of a derivative like-set. Springer Science + Business Media B.V., 2007 Generalized Jacobian nationallicence Characterization theorem nationallicence Restriction rule nationallicence Chain rule nationallicence Sum rule nationallicence Continuous selection nationallicence Páles Zsolt Institute of Mathematics, University of Debrecen, Pf. 12, 4010, Debrecen, Hungary aut Zeidan Vera Department of Mathematics, Michigan State University, 48824, East Lansing, MI, USA aut Set-Valued Analysis Springer Netherlands 15/4(2007-12-01), 331-375 0927-6947 15:4<331 2007 15 11228 https://doi.org/10.1007/s11228-007-0043-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11228-007-0043-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Páles Zsolt Institute of Mathematics, University of Debrecen, Pf. 12, 4010, Debrecen, Hungary aut NATIONALLICENCE 700 1- Zeidan Vera Department of Mathematics, Michigan State University, 48824, East Lansing, MI, USA aut NATIONALLICENCE 773 0- Set-Valued Analysis Springer Netherlands 15/4(2007-12-01), 331-375 0927-6947 15:4<331 2007 15 11228 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer