Directional convex extensions of the convex valued maps

• Autorzy: Duzce, S. A. , Guseinov, KH. G.
• Języki publikacji: EN

Abstrakty

EN

In this paper, the concept of directional convex extension of the convex valued maps is introduced. Necessary and sufficient conditions for the existence of the directional convex extension of the convex valued map are obtained.

Słowa kluczowe

PL

odwzorowanie wartości zadanej; pochodna zbioru

EN

set valued map; directional convex extension; derivative set

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2009
• Tom: Vol. 15, nr 1
• Strony: 129-138
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Duzce, S. A.

autor

Guseinov, KH. G.

• Anadolu University Department of Mathematics,

Bibliografia

• [1] Aubin, J.-P., Frankowska, H., Set Valued Analysis, Birkhauser, Boston, 1990.
• [2] Duzce, S. A., Convex continuation of the convex set valued -maps and applications to the differential inclusion theory (in Turkish), PhD thesis, Anadolu University, Eskisehir, 2003.
• [3] Guseinov, Kh. G., Duzce, S. A., Ozer, O., Convex extensions of the convex set valued maps, J. Math. Anal. Appl. 314(2) (2006), 672-688.
• [4] Guseinov, Kh. G., Duzce, S. A., Ozer, O., The construction of differential inclusions with prescribed attainable sets, J. Dyn. Control Systems 14(4) (2008), 441-452.
• [5] Guseinov, Kh. G., Ozer, O., Duzce, S. A., Maximal convex continuation for convex compact set valued map (in Turkish), Anadolu Univ. J. Sci. Tech. 3 (2002), 383 388.
• [6] Guseinov, Kh. G., Ushakov, V. N., The construction of differential inclusions with prescribed properties, Differ. Equ. 36 (2000), 488-496.
• [7] Hu, Sh., Papageorgiou, N. S., Handbook of Multivalued, Analysis. Vol. I. Theory. Kluwer Academic, Dordrecht, 1997.
• [8] Rockafellar, R. T., Convex Analysis, Princeton Math. Ser. 28, Princeton Univ. Press. N. J., 1970.