| 1. |
- Abramovich, Shoshana, et al.
(författare)
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General inequalities via isotonic subadditive functionals
- 2007
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 10:1, s. 15-28
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Tidskriftsartikel (refereegranskat)abstract
- In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Holder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.
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| 2. |
- Abramovich, Shoshana, et al.
(författare)
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Inequalities for averages of quasiconvex and superquadratic functions
- 2016
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 19:2, s. 535-550
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Tidskriftsartikel (refereegranskat)abstract
- For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.
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| 3. |
- Abramovich, Shoshana, et al.
(författare)
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On some new developments of Hardy-type inequalities
- 2012
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Ingår i: 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. - Melville, NY : American Institute of Physics (AIP). - 9780735411050 ; , s. 739-746
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Konferensbidrag (refereegranskat)abstract
- In this paper we present and discuss some new developments of Hardy-type inequalities, namely to derive (a) Hardy-type inequalities via a convexity approach, (b) refined scales of Hardy-type inequalities with other “breaking points” than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardy-type inequalities.
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| 4. |
- 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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| 5. |
- Abramovich, Shoshana, et al.
(författare)
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Some new estimates of the ‘Jensen gap’
- 2016
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Ingår i: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X. ; 2016
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Tidskriftsartikel (refereegranskat)abstract
- Let (μ,Ω) be a probability measure space. We consider the so-called ‘Jensen gap’ J(φ,μ,f)=∫ Ω φ(f(s))dμ(s)−φ(∫ Ω f(s)dμ(s)) for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.
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| 6. |
- Abramovich, Shoshana, et al.
(författare)
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Some new Hermite-Hadamard and Fejer type inequalities without convexity/concavity
- 2020
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Ingår i: Mathematical Inequalities & Applications. - : Element. - 1331-4343 .- 1848-9966. ; 23:2, s. 447-458
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss the Hermite-Hadamard and Fejer inequalities vis-a-vis the convexity concept. In particular, we derive some new theorems and examples where Hermite-Hadamard and Fejer type inequalities are satisfied without the assumptions of convexity or concavity on the actual interval [a,b]
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| 7. |
- Abramovich, Shoshana, et al.
(författare)
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Some new refined Hardy type inequalities with general kernels and measures
- 2010
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Ingår i: Aequationes Mathematicae. - : Springer Science and Business Media LLC. - 0001-9054 .- 1420-8903. ; 79:1-2, s. 157-172
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Tidskriftsartikel (refereegranskat)abstract
- We state and prove some new refined Hardy type inequalities using the notation of superquadratic and subquadratic functions with an integral operator Ak defined by, where k: Ω1 × Ω2 is a general nonnegative kernel, (Ω1, μ1) and (Ω2, μ2) are measure spaces and,. The relations to other results of this type are discussed and, in particular, some new integral identities of independent interest are obtained.
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| 8. |
- Abramovich, Shoshana, et al.
(författare)
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Some new scales of refined Hardy type inequalities via functions related to superquadracity
- 2013
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 16:3, s. 679-695
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Tidskriftsartikel (refereegranskat)abstract
- For the Hardy type inequalities the "breaking point" (=the point where the inequality reverses) is p = 1. Recently, J. Oguntoase and L. E. Persson proved a refined Hardy type inequality with a breaking point at p = 2. In this paper we prove a new scale of refined Hardy type inequality which can have a breaking point at any p ≥ 2. The technique is to first make some further investigations for superquadratic and superterzatic functions of independent interest, among which, a new Jensen type inequality is proved
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| 9. |
- 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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