On a Jansen type functional equation

• Autorzy: Smajdor W.
• Języki publikacji: EN

Abstrakty

EN

We investigate the functional equation [wzór] for f: M S, where M is an Abelian 2- and 3-divisible group and S is an abstract convex cone. The motivation for studying this equation came from results due to Tiberiu Trief [8] and Young Whan Lee [3], where equation (1) was considered with constants a = 3, b = 2 and a = 9 and b = 4, respectively.

Słowa kluczowe

EN

Jensen's functional equation; abstract convex cone; additive and quadratic functions; multifunctions

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2007
• Tom: Vol. 13, nr 1
• Strony: 19--31
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Smajdor W.

• Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland,

Bibliografia

• [1] Castaing, C., Valadier, M., Convex Analysis and Measumble Multifunctions, Lecture Notes in Math. 580, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
• [2] De Blasi, F .S., On differentiability of multifunctions, Pacific J. Math. 66 (1976),67-81.
• [3] Lee, Y. W., On the stability of a quadratic Jensen type functional equation, J. Math. Anal. Appl. 270 (2002), 590-601.
• [4] Radstrom, H., An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
• [5] Smajdor, W., On Jensen and Pexider functional eqvuations, Opuscula Math. 14 (1994), 169-178.
• [6] Smajdor, W ., Note on a Jensen type functional equation, Publ. Math. Debrecen 63( 4) (2003), 703-714.
• [7] Urbański, R., A generalization of Minkowski-Radstrom-Hormander theorem, Bull. Acad. Polon. Sci. ser. Sci. Math. Astronom. Phys. 24(9) (1976), 709-715.
• [8] Trif, T., Hyers-Ulam-Rassias stability of a Jensen type functional equation, J. Math. Anal. Appl. 250 (2000), 579-588.