Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality
The aim of this paper is to present connections between the Jensen and Hermite-Hadamard inequality.
The study includes convex functions of one and several variables. The basis of the research are convex
combinations with the common center.
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- [1] Bjelica, M., Refinement and converse of Brunk-Olkin inequality. Journal of Mathematical Analysis and Applications
272 (1998), 462-467.
- [2] Chen, F., A Note on Hermite-Hadamard inequalities for products of convex functions. Journal of Applied
Mathematics 2013 (2013), Article ID 935020.
- [3] Dragomir, S. S. and Pearce, Ch. E. M., Selected Topics on Hermite-Hadamard Inequalities and Applications.
RGMIA Monographs. Victoria University, Melbourne, AU, 2000.
- [4] Hadamard, J., Étude sur les propriétés des fonctions entières et en particulier d’une fonction considerée par
Riemann. Journal de Mathématiques Pures et Appliquées 58 (1893), 171-215.
- [5] Hermite, Ch., Sur deux limites d’une intégrale définie. Mathesis 3 (1883), 82.
- [6] Jensen, J. L. W. V., Om konvekse Funktioner og Uligheder mellem Middelværdier. Nyt tidsskrift for matematik. B.
16 (1905), 49-68.
- [7] Jensen, J. L. W. V., Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica 30
(1906), 175-193
- [8] Lyu, S. L., On the Hermite-Hadamard inequality for convex functions of two variables. Numerical Algebra,
Control and Optimization 4 (2014), 1-8.
- [9] Niculescu, C. P. and Persson, L. E., Convex Functions and Their Applications. Canadian Mathematical Society.
Springer, New York, USA, 2006.
- [10] Niculescu, C. P. and Persson, L. E., Old and new on the Hermite-Hadamard inequality. Real Analysis Exchange
29 (2003), 663-685.
- [11] Pavic, Z., Generalizations of Jensen-Mercer’s inequality. Journal of Pure and Applied Mathematics: Advances and
Applications 11 (2014), 19-36.
- [12] Pavic, Z., Extension of Jensen’s inequality to affine combinations. Journal of Inequalities and Applications 2014
(2014), Article 298.
- [13] Pecaric, J. E., A simple proof of the Jensen-Steffensen inequality. American Mathematical Monthly 91 (1984),
195-196.
- [14] Wang, J., Li, X., Feckan, M. and Zhou, Y., Hermite-Hadamard-type inequalities for Riemann-Liouville fractional
integrals via two kinds of convexity. Applicable Analysis 92 (2013), 2241-2253.
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