Results 1 to 10 of about 82 (75)

Generalized Jensen-Steffensen and related inequalities [PDF]

Journal of Mathematical Inequalities, 2015
We introduce a new tool for comparing two linear functionals that are positive on convex functions. We generalize Jensen-Steffensen and related inequalities.
Jakšetić, Julije, Pečarić, Josip, Praljak, Marjan   +2 more
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Jensen-Steffensen's and related inequalities for superquadratic functions [PDF]

Mathematical inequalities & applications, 2008
Refinements of Jensen-Steffensen's inequality, Slater-Pečarić's inequality and majorization theorems for superquadratic functions are presented.
Pečarić, Josip, Matić, Marko, Banić, Senka   +2 more
openaire   +3 more sources

Improvement of Jensen--Steffensen's inequality for superquadratic functions

Banach Journal of Mathematical Analysis, 2010
In this paper, improvements for superquadratic functions of Jensen-Steffensen's and related inequalities are discussed. For superquadratic functions which are not convex we get inequalities analog to Jensen-Steffensen's inequality for convex functions. For superquadratic functions which are convex (including many useful functions), we get improvements ...
Abramovich, Shoshana, Ivelic, Slavica, Pecaric, Josip E.   +2 more
openaire   +5 more sources

The Jensen-Steffensen inequality [PDF]

Mathematical Inequalities & Applications, 1998
New proofs of the Jensen-Steffensen and its inverse inequality given by the reviewer are presented.
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Jensen–Steffensen inequality for strongly convex functions [PDF]

Journal of Inequalities and Applications, 2018
The Jensen inequality for convex functions holds under the assumption that all of the included weights are nonnegative. If we allow some of the weights to be negative, such an inequality is called the Jensen-Steffensen inequality for convex functions. In this paper we prove the Jensen-Steffensen inequality for strongly convex functions.
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On the refinements of the Jensen-Steffensen inequality [PDF]

Journal of Inequalities and Applications, 2011
Abstract In this paper, we extend some old and give some new refinements of the Jensen-Steffensen inequality. Further, we investigate the log-convexity and the exponential convexity of functionals defined via these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals.
Iva Franjić, Sadia Khalid, ‎Josip Pečarić   +2 more
openaire   +2 more sources

On the refinements of the integral Jensen-Steffensen inequality [PDF]

Journal of Inequalities and Applications, 2013
Dans cet article, nous présentons des versions intégrales de certains résultats récemment prouvés qui affinent l'inégalité de Jensen-Steffensen. Nous prouvons la convexité n-exponentielle et la log-convexité des fonctions associées aux fonctions linéaires construites à partir des inégalités raffinées et prouvons également la propriété de monotonie des ...
Sadia Khalid, Josip ‎Pečarić
openaire   +2 more sources

Generalization of Jensen's and Jensen-Steffensen's inequalities by generalized majorization theorem [PDF]

Journal of mathematical inequalities, 2017
In this paper, we use generalized majorization theorem and give the generalizations of Jensen’s and Jensen-Steffensen’s inequalities. We present the generalization of converse of Jensen’s inequality. We give bounds for the identities related to the generalization of Jensen’s inequality by using ˇ Cebyˇsev functionals.
Khan, M. A., Khan, J., Pečarić, J.
openaire   +3 more sources

Generalizations of the Jensen-Steffensen and related inequalities

Open Mathematics, 2009
Abstract We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality are deduced as special cases from these general inequalities.
Pečarić, Josip, Matić, Marko, Klaričić Bakula, Milica   +2 more
openaire   +6 more sources

On exponential convexity, Jensen-Steffensen-Boas Inequality, and Cauchy's means for superquadratic functions [PDF]

Journal of Mathematical Inequalities, 2011
In this paper we define new means of Cauchy's type using some recently obtained results that refine the Jensen-Steffensen-Boas inequality for convex and superquadratic functions. Applying so called exp-convex method we interpret results in the form of exponentially convex or (as a special case) logarithmically convex functions.
Abramovich, Shoshana, Farid, Ghulam, Ivelić, Slavica, Pečarić, Josip   +3 more
openaire   +3 more sources