Hermite-Hadamard inequalities for convex set-valued functions

• Autorzy: Mitroi F. C. , Nikodem K. , Wąsowicz S.
• Języki publikacji: EN

Abstrakty

EN

The following version of the weighted Hermite-Hadamard inequalities for set-valued functions is presented: Let Y be a Banach space and F : [a, b]→cl(Y) be a continuous set-valued function. If F is convex, then (…) , where μ is a Borel measure on [a, b] and xμ is the barycenter of on [a, b]. The converse result is also given.

Słowa kluczowe

EN

convex set-valued function; Hermite-Hadamard inequality

PL

nierówność Hermite-Hadamarda

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 4
• Strony: 655--662
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Mitroi F. C.

• Department of Mathematics, University of Craiova, Street A. I. Cuza 13, 2000585 Craiova, Romania

autor

Nikodem K.

• Department of Mathematics and Computer Science, University of Bielsko-Biała, ul. Willowa 2, 43-309 Bielsko-Biała, Poland

autor

Wąsowicz S.

• Department of Mathematics and Computer Science, University of Bielsko-Biała, ul. Willowa 2, 43-309 Bielsko-Biała, Poland

Bibliografia

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• [6] C. P. Niculescu, L. -E. Persson, Convex Functions and their Applications. A Contemporary Approach, CMS Books in Mathematics vol. 23, Springer-Verlag, New York, 2006.
• [7] K. Nikodem, K-convex and K-concave set–valued functions, Zeszyty Nauk. Politech. Łódz. Mat. 559; Rozprawy Mat. 114., Łódź, 1989.
• [8] J. E. Pečarić, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Acad. Press, Inc., Boston, 1992.
• [9] B. Piątek, On convex and *-concave multifunctions, Ann. Polon. Math. 86 (2005), 165–170.
• [10] S. Rolewicz, Functional Analysis and Control Theory. Linear Systems, PWN – Polish Scientific Publishers & D. Reidel Publishing Company, Dordrecht/Boston/Lancaster/Tokyo, 1987.
• [11] E. Sadowska, Hadamard inequality and a refinement of Jensen inequality for set-valued functions, Results Math. 32 (1997), 332–337.