Results 1 to 10 of about 4,869 (94)

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
M. Klaričić Bakula
doaj   +11 more sources

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

Journal of Inequalities and Applications, 2011
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 ...
Khalid Sadia, Pečarić Josip, Franjić Iva   +2 more
doaj   +5 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.
Bakula Milica, Matić Marko, Pečarić Josip   +2 more
doaj   +8 more sources

Generalizations of Jensen-Steffensen and related integral inequalities for superquadratic functions

Open Mathematics, 2010
Abstract We present integral versions of some recently proved results which improve the Jensen-Steffensen and related inequalities for superquadratic functions. For superquadratic functions which are not convex we get inequalities analogous to the integral Jensen-Steffensen inequality for convex functions.
Abramovich Shoshana, Ivelić Slavica, Pečarić Josip   +2 more
doaj   +5 more sources

Chebyshev-Steffensen Inequality Involving the Inner Product

Mathematics, 2022
In this paper, we prove the Chebyshev-Steffensen inequality involving the inner product on the real m-space. Some upper bounds for the weighted Chebyshev-Steffensen functional, as well as the Jensen-Steffensen functional involving the inner product under
Milica Klaričić Bakula, Josip Pečarić   +1 more
doaj   +4 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 ...
Shoshana Abramovich, Josip Pecaric
exaly   +7 more sources

A companion to Jensen-Steffensen's inequality

Journal of Approximation Theory, 1985
Suppose that f is a convex function on (a,b).
Josip Pecaric
exaly   +3 more sources

A variant of Jensen–Steffensen's inequality and quasi-arithmetic means

Journal of Mathematical Analysis and Applications, 2005
A variant of Jensen-Steffensen's inequality is proved. Necessary and sufficient conditions for the equality in Jensen-Steffensen's inequality are established. Several inequalities involving more than two monotonic functions and generalized quasi-arithmetic means with not only positive weights are proved.
S Abramovich, Milica Klaričić Bakula, M Matic   +2 more
exaly   +5 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
semanticscholar   +4 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.
P. Bullen
openaire   +3 more sources