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Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications

Journal of Inequalities and Applications
AbstractIn this paper we give a necessary and sufficient condition for the discrete Jensen inequality to be satisfied for real (not necessarily nonnegative) weights. The result generalizes and completes the classical Jensen–Steffensen inequality. The validity of the strict inequality is studied. As applications, we first give the form of our result for
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Jensen-Steffensen type inequality for integrals with respect to bi-capacities

, 2021
The bipolar pan-integral as new type of integral based on bi-capacities is introduced in the thesis. The main purpose of the thesis is to establish conditions under which the Jensen type inequality is valid for: the discrete bipolar pseudo-integral, the new bipolar Choquet g-integral, the bipolar Shilkret and the bipolar Sugeno integral.
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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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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
Milica Klaricic Bakula, Anita Matkovic, Josip Pecaric   +2 more
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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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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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