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Języki publikacji
Abstrakty
We present Hermite-Hadamard type inequalities for Wright-convex, strongly convex and strongly Wright-convex functions of several variables defined on simplices.
Czasopismo
Rocznik
Tom
Strony
411--419
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- University of Bielsko-Biała Department of Mathematics and Computer Science Willowa 2, 43-309 Bielsko-Biała, Poland
autor
- University of Bielsko-Biała Department of Mathematics and Computer Science Willowa 2, 43-309 Bielsko-Biała, Poland
Bibliografia
- [1] M. Bessenyei, The Hermite-Hadamard inequality on simplices, Amer. Math. Monthly 115 (2008), 339-345.
- [2] S.S. Dragomir, C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2002.
- [3] A. Guessab, G. Schmeisser, Convexity results and sharp error estimates in approximate multivariate integration, Math. Comp. 73 (2004), 1365-1384.
- [4] J.B. Hiriart-Urruty, C. Lemarechal, Fundamentals of convex analysis, Springer-Verlag, Berlin Heidelberg, 2001.
- [5] N. Merentes, K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010), 193-199.
- [6] N. Merentes, K. Nikodem, S. Rivas, Remarks on strongly Wright-convex functions, Ann. Polon. Math. 102 (2011), 271-278.
- [7] E. Neuman, Inequalities involving multivariate convex functions II, Proc. Amer. Math. Soc. 109 (1990), 965-974.
- [8] C.T. Ng. Functions generating Schur-convex sums, [in:] General inequalities, 5 (Ober-wolfach, 1986), vol. 80 of Internat. Schriftenreihe Numer. Math., pp. 433-438. Birkhauser, Basel, 1987.
- [9] C.P. Niculescu, L.E. Persson, Convex Functions and Their Applications. A Contemporary Approach, Springer, New York 2006.
- [10] A. Olbryś, On some inequalities equivalent to the Wright convexity, submitted.
- [11] B. T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. 7 (1966), 72-75.
- [12] Sz. Wąsowicz, A. Witkowski, On some inequality of Hermite-Hadamard type, Opuscula Math. 32 (2012), 591-600.
- [13] Sz. Wąsowicz, Hermite-Hadamard-type inequalities in the approximate integration, Math. Inequal. Appl. 11 (2008), 693-700.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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