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1
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Refinement of the Jensen integral inequality

100%
Sever Dragomir S., Adil Khan M., Abathun A.
Open Mathematics
|
2016
|
tom 14
|
nr 1
221-228
EN
In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.
2
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Generalizations of Jensen-Steffensen and related integral inequalities for superquadratic functions

100%
Abramovich S., Ivelić S., Pečarić J.
Open Mathematics
|
2010
|
tom 8
|
nr 5
937-949
EN
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. Therefore, we get refinements of all the results which use only the convexity of these functions. One of the inequalities that we obtain for a superquadratic function φ is $$ \bar y \geqslant \phi \left( {\bar x} \right) + \frac{1} {{\lambda \left( \beta \right) - \lambda \left( \alpha \right)}}\int_\alpha ^\beta {\phi \left( {\left| {f\left( t \right) - \bar x} \right|} \right)d\lambda \left( t \right)} $$, where $$ \bar x = \frac{1} {{\lambda \left( \beta \right) - \lambda \left( \alpha \right)}}\int_\alpha ^\beta {f\left( t \right)d\lambda \left( t \right)} $$ and $$ \bar y = \frac{1} {{\lambda \left( \beta \right) - \lambda \left( \alpha \right)}}\int_\alpha ^\beta {\phi \left( {f\left( t \right)} \right)d\lambda \left( t \right)} $$ which under suitable conditions like those satisfied by functions of power equal or more than 2, is a refinement of the Jensen-Steffensen-Boas inequality. We also prove related results of Mercer’s type.
3
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Generalizations of the Jensen-Steffensen and related inequalities

100%
Bakula M., Matić M., Pečarić J.
Open Mathematics
|
2009
|
tom 7
|
nr 4
787-803
EN
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.
4
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Some new inequalities of Hermite-Hadamard type for GA-convex functions

100%
Dragomir S. S.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2018
|
tom 72
|
nr 1
EN
Some new inequalities of Hermite-Hadamard type for GA-convex functions defined on positive intervals are given. Refinements and weighted version of known inequalities are provided. Some applications for special means are also obtained.
5
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Differential subordination and convexity criteria of integral operators

100%
Chandrashekar R., Keong Lee S., Subramanian K. G.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1509-1516
EN
A significant connection between certain second-order differential subordination and subordination of f′(z) is obtained. This fundamental result is next applied to investigate the convexity of analytic functions defined in the open unit disk. As a consequence, criteria for convexity of functions defined by integral operators are determined. Connections are also made to earlier known results.
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