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Yıl 2016, Cilt: 4 Sayı: 1, 69 - 76, 15.04.2016

Zlatko Pavić

https://doi.org/10.36753/mathenot.421405
Cited By: 2

Öz

Kaynakça

  • [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

Yıl 2016, Cilt: 4 Sayı: 1, 69 - 76, 15.04.2016

Zlatko Pavić

https://doi.org/10.36753/mathenot.421405
Cited By: 2

Öz

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.

Anahtar Kelimeler

convex combination convex function simplex Jensen’s inequality

Kaynakça

  • [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
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Zlatko Pavić

Yayımlanma Tarihi 15 Nisan 2016
Gönderilme Tarihi 16 Şubat 2015
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 1

Kaynak Göster

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. Nisan 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, sy. 1 (Nisan 2016): 69-76. https://doi.org/10.36753/mathenot.421405.
EndNote Pavić Z (01 Nisan 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, c. 4, sy. 1, ss. 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 (Nisan 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, c. 4, sy. 1, 2016, ss. 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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