The Steffensen-Popoviciu measures in the context of quasiconvex functions
Details, various extensions and applications of this results are available in numerous books; see, for example, Niculescu and Persson [18], Pečarić, Proschan and Tong [21], Phelps [22] and Simon [25]. Starting with the pioneering work of J. F. Steffensen
Constantin P. Niculescu, M. Stănescu
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23rd Congress of the European Hematology Association Stockholm, Sweden, June 14‐17, 2018
HemaSphere, Volume 2, Issue S1, Page 1-1113, June 2018.
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Uniform Treatment of Integral Majorization Inequalities with Applications to Hermite-Hadamard-Fejér-Type Inequalities and f-Divergences. [PDF]
Horváth L.
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Jensen, Hölder, Minkowski, Jensen-Steffensen and Slater-Pečarić inequalities derived through N-quasiconvexity [PDF]
Summary: Jensen, Hölder, Minkowski, Jensen-Steffensen and Slater-Pečarić type inequalities derived by the properties of \(\gamma\)-quasiconvex functions that we deal with here, can be seen as analog to these for superquadratic functions and refinements of these for convex functions.
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Heart Disease and Stroke Statistics-2023 Update: A Report From the American Heart Association. [PDF]
Tsao CW +43 more
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A variant of Jensen-Steffensen's inequality for convex and superquadratic functions
A variant of Jensen-Steffensen's inequality is considered for convex and for superquadratic functions. Consequently, inequalities for power means involving not only positive weights have been established.
Banić, Senka, Klaričić Bakula, Milica
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Heart Disease and Stroke Statistics-2021 Update: A Report From the American Heart Association. [PDF]
Virani SS +39 more
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Cauchy type means related to the converse Jensen-Steffensen inequality
In this paper we apply so called exp-convex method to the converse Jensen-Steffensen inequality in order to interpret it in the form of exponentially convex functions. The outcome is a new class of Cauchy type means and some new interesting inequalities related to them.
Ivelić, Slavica +2 more
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Levinson's type generalization of the Jensen inequality and its converse for real Stieltjes measure. [PDF]
Mikić R, Pečarić J, Rodić M.
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Jensen-Steffensen type inequality for integrals with respect to bi-capacities
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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