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Improvement of Jensen, Jensen-Steffensen's, and Jensen's functionals related inequalities for various types of convexity

In this paper we deal with improvement of Jensen, Jensen-Steffensen's and Jensen's functionals related inequalities for uniformly convex, phi-convex and superquadratic functions.
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Mercer type variants of the Jensen–Steffensen inequality

Rocky Mountain Journal of Mathematics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khan, Asif R., Rubab, Faiza
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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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On the Jensen-Steffensen inequality for generalized convex functions [PDF]

Periodica Mathematica Hungarica, 2007
Jensen-Steffensen type inequalities for P-convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev's inequality and several variants of Hölder's inequality with weights satisfying the conditions as in the Jensen-Steffensen inequality. A few well known inequalities for
Pečarić, Josip, Klaričić Bakula, Milica, Matković, Anita   +2 more
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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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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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Jensen-Steffensen Inequality: Accentuate the Negative

2023
One can say that the Jensen-Steffensen inequality is "the ugly sister" of the Jensen inequality: not much admired and usually "not invited to the party". Our goal here is to show that "she" has many hidden beauties and that "she" can proudly walk hand in hand with her well-known sister.
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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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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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