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Year 2016, Volume: 4 Issue: 1, 69 - 76, 15.04.2016
https://doi.org/10.36753/mathenot.421405

Abstract

References

  • [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. Affiliations

Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality

Year 2016, Volume: 4 Issue: 1, 69 - 76, 15.04.2016
https://doi.org/10.36753/mathenot.421405

Abstract

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.

References

  • [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. Affiliations
There are 14 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Zlatko Pavić This is me

Publication Date April 15, 2016
Submission Date February 16, 2015
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Pavić, Z. (2016). Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality. Mathematical Sciences and Applications E-Notes, 4(1), 69-76. https://doi.org/10.36753/mathenot.421405
AMA Pavić Z. Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality. Math. Sci. Appl. E-Notes. April 2016;4(1):69-76. doi:10.36753/mathenot.421405
Chicago Pavić, Zlatko. “Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 69-76. https://doi.org/10.36753/mathenot.421405.
EndNote Pavić Z (April 1, 2016) Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality. Mathematical Sciences and Applications E-Notes 4 1 69–76.
IEEE Z. Pavić, “Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 69–76, 2016, doi: 10.36753/mathenot.421405.
ISNAD Pavić, Zlatko. “Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 69-76. https://doi.org/10.36753/mathenot.421405.
JAMA Pavić Z. Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality. Math. Sci. Appl. E-Notes. 2016;4:69–76.
MLA Pavić, Zlatko. “Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 69-76, doi:10.36753/mathenot.421405.
Vancouver Pavić Z. Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality. Math. Sci. Appl. E-Notes. 2016;4(1):69-76.

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