The Jensen-Mercer Inequality with Infinite Convex Combinations

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

The paper deals with discrete forms of double inequalities related to convex functions of one variable.

Keywords:

double inequality, infinite convex combination Jensen-Mercer inequality,

[1] Hadamard, J., Étude sur les propriétés des fonctions entières et en particulier d’une fonction considerée par Riemann, J. Math. Pures Appl., 58(1893), 171-215.
[2] Hermite, Ch., Sur deux limites d’une intégrale définie, Mathesis, 3(1883), 82.
[3] Iveli´c, S., Matkovic, A. and Pecaric, J. E., On a Jensen-Mercer operator inequality, Banach J. Math. Anal., 5(2011), 19-28.
[4] Jensen, J. L.W. V., Om konvekse Funktioner og Uligheder mellem Middelværdier, Nyt Tidsskr. Math. B, 16(1905), 49-68.
[5] Khan, M. A., Khan, G. A., Jameel, M., Khan, K. A. and Kilicman, A., New refinements of Jensen-Mercer’s inequality J. Comput. Theor. Nanosci., 12(2015), 4442-4449.
[6] Matkovic, A., Peˇcari´c, J. and Peri´c, I., A variant of Jensen’s inequality of Mercer’s type for operators with applications, Linear Algebra Appl., 418(2006), 551-564.
[7] Mercer, A. McD., A variant of Jensen’s inequality, JIPAM, 4(2003), Article 73.
[8] Niezgoda, M., A generalization of Mercer’s result on convex functions, Nonlinear Anal., 71(2009), 2771-2779.
[9] Pavic, Z., Convex function and its secant, Adv. Inequal. Appl., 2015(2015), Article 5.
[10] Pavic, Z., Generalizations of Jensen-Mercer’s inequality, J. Pure Appl. Math. Adv. Appl., 11(2014), 19-36.
[11] Pavic Z., Geometric and analytic connections of the Jensen and Hermite-Hadamard inequality, Math. Sci. Appl. E-Notes, 4(2016), 69-76.
[12] Pavic, Z., Inequalities with infinite convex combinations, submitted to FILOMAT.