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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.
2
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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.
3
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Extensions and improvements of Sherman’s and related inequalities forn-convex functions

100%
Bradanović S. I., Pečarić J.
Open Mathematics
|
2017
|
tom 15
|
nr 1
936-947
EN
This paper gives extensions and improvements of Sherman’s inequality for n-convex functions obtained by using new identities which involve Green’s functions and Fink’s identity. Moreover, extensions and improvements of Majorization inequality as well as Jensen’s inequality are obtained as direct consequences. New inequalities between geometric, logarithmic and arithmetic means are also established.
4
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Refinement of the Jensen integral inequality

81%
Sever Dragomir S., Adil Khan M., Abathun A.
Open Mathematics
|
2016
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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.
5
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Grüss-type bounds for covariances and the notion of quadrant dependence in expectation

81%
Egozcue M., García L., Wong W.-K., Zitikis R.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1288-1297
EN
We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate distributions that are QDE but not QD. Such results play important roles in decision making under uncertainty, and particularly in areas such as economics, finance, and insurance.
6
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Integral inequalities involving generalized Erdélyi-Kober fractional integral operators

62%
Baleanu D., Purohit S. D., Prajapati J. C.
Open Mathematics
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2016
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tom 14
|
nr 1
89-99
EN
Using the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.
7
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A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications

62%
Alomari M. W.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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2016
|
tom 15
EN
A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral [...] ∫abf(t) du(t) $\int_a^b {f(t)\;du(t)} $ , where f is assumed to be of r-H-Hölder type on [a, b] and u is of bounded variation on [a, b], is proved. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.
8
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Some new inequalities of Hermite-Hadamard type fors-convex functions with applications

62%
Khan M. A., Chu Y., Khan T. U., Khan J.
Open Mathematics
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2017
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tom 15
|
nr 1
1414-1430
EN
In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.
9
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On the more general Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals

52%
Set E., Mumcu I., Özdemir M. E.
Topological Algebra and its Applications
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2017
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tom 5
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nr 1
67-73
10
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Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators

52%
Set E., Gözpinar A.
Topological Algebra and its Applications
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2017
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tom 5
|
nr 1
55-62
EN
In this present work, the authors establish a new integral identity involving generalized fractional integral operators and by using this fractional-type integral identity, obtain some new Hermite-Hadamard type inequalities for functions whose first derivatives in absolute value are convex. Relevant connections of the results presented here with those earlier ones are also pointed out.
11
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Approximating real Pochhammer products: a comparison with powers

52%
Lampret V.
Open Mathematics
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2009
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tom 7
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nr 3
493-505
EN
Accurate estimates of real Pochhammer products, lower (falling) and upper (rising), are presented. Double inequalities comparing the Pochhammer products with powers are given. Several examples showing how to use the established approximations are stated.
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