| 1. |
- Abramovich, Shoshana, et al.
(författare)
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On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities
- 2015
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 18:2, s. 615-627
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we deal with γ -quasiconvex functions when −1γ 0, to derive sometwo-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalitiesfor 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functionswith Jensen type inequalities for superquadratic functions and we extend the result obtained forγ -quasiconvex functions to more general classes of functions.
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| 2. |
- Abramovich, Shoshana, et al.
(författare)
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Some new scales of refined Jensen and Hardy type inequalities
- 2014
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 17:3, s. 1105-1114
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Tidskriftsartikel (refereegranskat)abstract
- Some scales of refined Jensen and Hardy type inequalities are derived and discussed. The key object in our technique is ? -quasiconvex functions K(x) defined by K(x)x-? =? (x) , where Φ is convex on [0,b) , 0 < b > ∞ and γ > 0.
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| 3. |
- Lukkassen, Dag, et al.
(författare)
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Some sharp inequalities for multidimensional integral operators with homogenous kernel : an overview and new results
- 2016
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 19:2, s. 551-564
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Tidskriftsartikel (refereegranskat)abstract
- One goal of this paper is to point out the fact that a big number of inequalities provedfrom time to time in journal publications, both one-dimensional and multi-dimensional, are particularcases of some general results for integral operators with homogeneous kernels, includingin particular, the statements on sharp constants.Some new multidimensional Hardy-Hilbert type inequalities are derived. Moreover, anew multidimensional P´olya-Knopp inequality is proved and some examples of applications arederived from this result. The constants in all inequalities are sharp.
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| 4. |
- Persson, Lars-Erik, et al.
(författare)
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Quasi-monotone weight functions and their characteristics and applications
- 2012
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 15:3, s. 685-705
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Tidskriftsartikel (refereegranskat)abstract
- A weight function w(x) on (0,l) or (l,infinity), is said to be quasi-monotone if w(x)x(-a0) <= C(0)w(y)y(-a0) either for all x <= y or for all y <= x, for some a(0) is an element of R, C-0 >= 1. In this paper we discuss, complement and unify several results concerning quasi-monotone functions. In particular, some new results concerning the close connection to index numbers and generalized Bary-Stechkin classes are proved and applied. Moreover, some new regularization results are proved and several applications are pointed out, e. g. in interpolation theory, Fourier analysis, Hardy-type inequalities, singular operators and homogenization theory.
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