PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2007 | Vol. 36, no 4 | 911-924
Tytuł artykułu

Generalized directional derivatives for locally Lipschitz functions which satisfy Leibniz rule

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper a concept of a generalized directional derivative, which satisfies Leibniz rule is proposed for locally Lipschitz functions, defined on an open subset of a Banach space. Although Leibniz rule is of less importance for a subdifferential calculus, it is of course of some theoretical interest to know about the existence of generalized directional derivatives which satisfy Leibniz rule. The proposed concept of generalized directional derivatives is adopted from the work of D. R. Sherbert (1964) who determined all point derivations for the Banach algebra of Lipschitz functions over a complete metric space.
Wydawca

Rocznik
Strony
911-924
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, PL-61-614 Poznań, Poland, grz@amu.edu.pl
Bibliografia
  • ARENS, R. and EELLS, J., JR. (1956) On embedding uniform and topological spaces. Pacific Journ. Math., 6, 397-403.
  • BOUGUENAYA, Y. and FAIRLIE, D.B. (1986) A finite difference scheme with a Leibniz rule. Journ. of Physics. A. Mathematical and Theoretical 19, 1049-1053.
  • CLARKE, F.H. (1989) Optimization and Nonsmooth Analysis. CRM, Université de Montréal, Quebec, Canada.
  • DEMYANOV, V.F. and PALLASCHKE, D. (1997) Point Derivations for Lipschitz Functions and Clarke's generalized Derivative. Applicationes Mathematicae 24 (4), 465-467.
  • DOLECKI, S. and KURCYUSZ, ST. (1978) On Φ-convexity in extremal problems. SIAM J. Control Optimization 16 (2) , 277-300.
  • DUNFORD, N. and SCHWARTZ, J.T. (1957) Linear Operators: Part I. Interscience Publishers, Inc., New York.
  • EBERHARD, A. and NYBLOM, M. (1998) Jets, generalised convexity, proximal normality and differences of functions. Nonlinear Anal. 34 (3), 319-360.
  • HÖRMANDER, L. (1954) Sur la fonction d'appui des ensembles convexes dans un espace localement convexe. Ark. Math. 3, 181-186.
  • MORDUKHOVICH, B. (2006) Variational analysis and generalized differentiation I - Basic theory. Grundl. der Mathem. Wissenschaften 330, Springer-Verlag, Berlin.
  • PALLASCHKE, D. and URBAŃSKI, R. (2002) Pairs of Compact Convex Sets -Fractional Arithmetic with Convex Sets. Mathematics and its Applications 548, Kluwer Acad. Publ. Dordrecht.
  • PALLASCHKE, D., RECHT, P. and URBAŃSKI, R. (1987) On Extensions of Second-Order Derivative. Bull. Science Soc. Polon. 35 (11-12), 751-763.
  • PALLASCHKE, D., RECHT, P. and URBAŃSKI, R. (1991) Generalized Derivatives for Non-Smooth Functions. Com. Mathematicae XXXI, 97-114.
  • PALLASCHKE, D. and ROLEWICZ, S. (1997) Foundations of Mathematical Optimization - Convex Analysis without Linearity. Mathematics and its Applications, Kluwer Acad. Publ, Dordrecht.
  • ROCKAFELLAR, R.T.(1970) Convex Analysis. Princeton University Press, Princeton, New Jersey.
  • ROLEWICZ, S. (2003) Φ-convex functions defined on metric spaces. Journ. of Math. Sci. (N. Y.) 115 (5), 2631-2652.
  • SHERBERT, D.R. (1964) The structure of ideals and point derivations in Banach Algebras of Lipschitz functions. Trans AMS 111, 240-272.
  • SINGER, I. and WERMER, J. (1955) Derivations on commutative normed algebras. Math. Ann. 129, 260-264.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0026-0006
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.