Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Cover of the book
Tytuł książki

Delta-convex mappings between Banach spaces and applications

Autorzy

L. L. Veselý L. Zajíček

Seria

Rozprawy Matematyczne tom/nr w serii: 289 wydano: 1989

Zawartość

Pełne teksty:
rm28901.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS
0. Introduction and notations...................................................5
1. Basic properties of delta-convex mappings.........................8
2. Delta-convex curves..........................................................15
3. Differentiability of delta-convex mappings.........................17
   A. First derivative...............................................................17
   B. Second derivative of mappings $F: R^n → Y$...............23
4. Superpositions and inverse mappings..............................26
5. Inverse mappings in finite-dimensional case.....................31
6. Examples and applications................................................34
   A. Three counterexamples.................................................34
   B. Nemyckii and Hammerstein operators............................36
   C. Weak solution of a differential equation.........................38
   D. Quasidifferentiable functions and mappings..................41
7. Some open problems........................................................44
References...........................................................................47

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 289

Liczba stron

48

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCLXXXIX

Daty

wydano
1989

Twórcy

autor
L. L. Veselý
  • aculty of Mathematics and Physics, Charles University, Sokolovski 83, 186 00 Praha 8, Czechoslovakia
autor
L. Zajíček
  • Faculty of Mathematics and Physics, Charles University, Sokolovski 83, 186 00 Praha 8, Czechoslovakia

Bibliografia

  • [1] A. D. Aleksandrov, Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it, Uch. Zap. Leningrad. Gos. Univ. Ann. Ser. Math. 6 (1939), 3-35 (in Russian).
  • [2] A. D. Aleksandrov, On surfaces represented as the difference of convex functions, Izv. Akad. Nauk. Kaz. SSR 60, Ser. Math. Mekh. 3 (1949), 3-20 (in Russian).
  • [3] A. D. Aleksandrov, Surfaces represented by the differences of convex functions, Dokl. Akad. Nauk SSSR (N. S.) 72 (1950), 613-616 (in Russian).
  • [4] N. Aronszajn, Differentiability of Lipschitzian mappings between Banach spaces. Studia Math. 57 (1976), 147-190.
  • [5] M. G. Arsove, Functions representable as the difference of subharmonic functions, Trans. Amer. Math. Soc. 75 (1953), 327-365.
  • [6] J. M. Borwein, Generic differentiability of order-bounded convex operators, J. Austral. Math. Soc. Ser. B 28 (1986), 22-29.
  • [7] N. Bourbaki, Éleménts de Mathématique, Variétés différentielles et analytiques, Paris 1967, 1971.
  • [8] H. Busemann and W. Feller, Krümmungseigenschaften konvexer Flächen, Acta Math. 66 (1936), 1-47.
  • [9] H. Cartan, Calcul différentiel, Forms différentielles, Paris 1967.
  • [10] F. H. Clarke, On the inverse function theorem, Pacific J. Math. 67 (1976), 97-102.
  • [11] V. F. Demjanov and A. M. Rubinov, On quasi-differentiable functionals, Dokl. Akad. Nauk SSSR 250 (1980), 21-25 (in Russian).
  • [12] V. F. Demjanov and A. M. Rubinov, On quasi-differentiable mappings, Math. Operations-forsch. u. Stat. ser. Optimization 14 (1983), 3-21.
  • [13] V. F. Demjanov and L. V. Vasiljev, Nondifferentiable Optimization, Springer-Verlag, New York 1985.
  • [14] J. Diestel and J. J. Uhl, Jr, The Radon-Nikodym theorem for Banach spaces valued measures. Rocky Mountain J. Math. 6 (1976), 1-46.
  • [15] N. Dunford and J. T. Schwartz, Linear Operators, 1. General theory, New York 1958.
  • [16] M. Fabián and D. Preiss, On the Clarke's generalized Jacobian, Proceedings or the 14-th Winter school on abstract analysis, to appear in Supplemento ai Rendiconti del Circolo Mathematico di Palermo.
  • [17] S. Fučik, Solvability of Nonlinear Equations and Boundary Value Problems, Prague 1980.
  • [18] P. Hartman, On functions representable as a difference of convex functions, Pacific J. Math. 9 (1959), 707-713.
  • [19] J. -B. Hiriart-Urruty, Generalized differentiability, duality and optimization for problems dealing with differences of convex functions, preprint.
  • [20] Hoàng Tuy, Global minimization of a difference of two convex functions, Lecture Notes in Econom. and Math. Systems 226, Springer-Verlag 1984, 98-118.
  • [21] Ch. O. Kiselman, Fonctions delta-convexes, delta-sousharmoniques et delta-plurisoushar-moniques, Lecture Notes in Mathematics 578, Springer-Verlag 1977, 93-107.
  • [22] K. Kuratowski, Topology, Vol. I (transl.), Academic Press, New York 1966.
  • [23] E. M. Landis, On functions representable as the difference of two convex functions, Dokl. Akad. Nauk SSSR (N. S.) 80 (1951), 9-11.
  • [24] J. Lukeš, J. Malý and L. Zajíček, Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Mathematics 1189, Springer-Verlag, 1986.
  • [25] F. Mignot, Contrôle dans les inéquations variatonelles elliptiques, J. Functional Analysis 22 (1976), 130-185.
  • [26] A. Nijenhuis, Strong derivatives and inverse mappings, Amer. Math. Monthly 81 (1974), 969-980.
  • [27] A. V. Pogorelov, Surfaces of hounded extrinsic curvature, 1956 (in Russian).
  • [28] B. H. Pourciau, Analysis and optimization of Lipschitz continuous mappings. J. Optim. Theory Appl. 22 (1977), 311-351.
  • [29] D. Preiss and L. Zajíček, Fréchet differentiation of convex functions in a Banach space with a separable dual, Proc. Amer. Math. Soc. 91 (1984), 202-204.
  • [30] D. Preiss and L. Zajíček, Stronger estimates of smallness of sets of Fréchet nondifferentiability of convex functions, Proceedings of the 11-th Winter school on Abstract Analysis, in Supplemento ai Rend. Circ. Mat. Palermo (2) no. 3 (1984), 219-223.
  • [31] A. W. Roberts and D. E. Varberg, Convex functions, New York and London 1973.
  • [32] A. Shapiro, On functions representable as a difference of two convex functions in inequality constrained optimization, Research report University of South Africa (1983).
  • [33] M. M. Vajnberg, Variational methods for the study of nonlinear operators (in Russian), Moscow 1956, English translation: Holden-Day, San Francisci 1964.
  • [34] L. Veselý, On the multiplicity points of monotone operators on separable Banach spaces. Comment. Math. Univ. Carolinae 27 (1986), 551-570.
  • [35] L. Veselý, A short proof of a theorem on compositions of d.c. mappings, to appear in Proc. Amer. Math. Soc.
  • [36] L. Veselý, On the multiplicity points of monotone operators on separable Banach spaces, II, Comment. Math. Univ. Carolinae 28 (1987), 295-299.
  • [37] L. Zajíček, On the differentiation of convex functions in finite and infinite dimensional spaces, Czechoslovak Math. J. 29 (1979), 340-348.
  • [38] L. Zajíček, On differentiation of metric projections in finite dimensional Banach spaces, Czechoslovak Math. J. 33 (1983), 325-336.
  • [39] V. A. Zalgaller, On the representation of a function of two variables as the difference of convex functions, Vestn. Leningrad. Univ. Ser. Mat. Mekh. 18 (1963), 44-45 (in Russian).

Języki publikacji

EN

Uwagi

Identyfikator YADDA

bwmeta1.element.zamlynska-f664bd7a-845c-42c8-b543-2b96d75206ba

Identyfikatory

ISBN
83-01-09395-1
ISSN
0012-3862

Kolekcja

DML-PL
Zawartość książki

rozwiń roczniki

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.