Results 51 to 60 of about 86 (65)

Converse Jensen–Steffensen inequality

Aequationes mathematicae, 2011
In this paper we prove a converse to the Jensen-Steffensen inequality and two inequalities complementary to the Jensen-Steffensen inequality. We apply so called exp-convex method in order to interpret our results in the form of exponentially convex functions. The outcome is a number of new interesting inequalities as well as some new Cauchy type means.
Klaričić Bakula, Milica, Ivelić Bradanović, Slavica, Pečarić, Josip   +2 more
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A counterpart to Jensen-Steffensen's inequality

Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, 2003
In this note a companion inequality to the Jensen-Steffensen inequality is ...
Pečarić, Josip, Elezović, Neven
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A Simple Proof of the Jensen-Steffensen Inequality

The American Mathematical Monthly, 1984
(1984). A Simple Proof of the Jensen-Steffensen Inequality. The American Mathematical Monthly: Vol. 91, No. 3, pp. 195-196.
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Jensen-Steffensen Inequality: Accentuate the Negative

2023
Let f:I→R, where I is an interval in ℝ, be a convex function on I, and x=(x₁,⋯,x_{n})∈Iⁿ. If p=(p₁,⋯,p_{n}) is a nonnegative real n-tuple such that P_{n}=∑_{i=1}ⁿp_{i}>0 then the well-known Jensen inequality f((1/(P_{n}))∑_{i=1}ⁿp_{i}x_{i})≤(1/(P_{n}))∑_{i=1}ⁿp_{i}f(x_{i}) jen holds.
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Jensen–Steffensen inequality for diamond integrals, its converse and improvements via Green function and Taylor’s formula

Aequationes mathematicae, 2018
In [Nonlinear Anal., Real World Appl. 7, No. 3, 395--413 (2006; Zbl 1114.26004)], \textit{Q. Sheng} et al. introduced the combined dynamic derivative, also called diamond \(\alpha\)-dynamic derivative \((\alpha\in[0,1])\). Using the delta and nabla derivatives due to \textit{S.
Ammara Nosheen, Rabia Bibi, Josip Pečarić   +2 more
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On some general inequalities of the Jensen-Steffensen type

2008
We present a pair of general inequalities related to the Jensen-Steffensen inequality for convex functions. We show that the discrete Jensen-Steffensen inequality, as well as a discrete Slater type inequality, can be obtained from these general inequalities as their special cases. We also prove that one of our general companion inequalities, under some
Klaričić Bakula, Milica, Matić, Marko, Pečarić, Josip   +2 more
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Conversions of the Jensen-Steffensen and Jensen-Mercer inequalities

2010
We establish conversions of the Jensen-Steffensen and Jensen-Mercer inequalities. We also use so caled exp-convex method to obtain some new inequalities related to those converse inequalities.
Klaričić Bakula, Milica, Ivelić Bradanović, Slavica, Pečarić, Josip   +2 more
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Generalization of Jensen's and Jensen- Steffensen's inequalities and their converses by Hermite's polynomial and majorization theorem

Advances in Mathematics, 2015
In this paper, using majorization theorems and Hermite's interpolating polynomials we obtain results concerning Jensen's and Jensen- Steffensen's inequalities and their converses in both the integral and the discrete case. We give bounds for identities related to these inequalities by using \v{; ; ; C}; ; ; eby\v{; ; ; s}; ; ; ev functionals.
Pečarić, Josip, Vukelić, Ana, Aras-Gazić, Gorana   +2 more
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On the bounds for the normalized Jensen functional and Jensen-Steffensen inequality

2016
We consider the inequalities for normalized Jensen functional, recently introduced by S.S. Dragomir. We give an alternative proof of such inequalities and prove another similar result for the case when f is a convex function on an interval in the real line, while p and q satisfy the conditions for Jensen-Steffensen inequality.
Barić, Josipa, Pečarić, Josip
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Jensen-Steffensen inequality: old and new

2016
{;Let $I$ be an interval in $\mathbb{;R};$ and $f:I\rightarrow \mathbb{;R};$ a convex function on $I$.\ If $\boldsymbol{;\xi };=\left( \xi _{;1};, \cdots , \xi _{;m};\right) $ is any $m$-tuple in $I^{;m};$ and $\boldsymbol{;p};=\left( p_{;1};, \cdots , p_{;m};\right) $ any nonnegative $m$-tuple such that $% \sum_{;i=1};^{;m};p_{;i};>0$, then the well ...
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