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| 2. |
- Abramovich, S., et al.
(författare)
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Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities
- 2018
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Ingår i: Mathematical Inequalities & Applications. - : Element D.O.O.. - 1331-4343 .- 1848-9966. ; 21:3, s. 759-772
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Tidskriftsartikel (refereegranskat)abstract
- In this paper extensions and refinements of Hermite-Hadamard and Fejer type inequalities are derived including monotonicity of some functions related to the Fejer inequality and extensions for functions, which are 1-quasiconvex and for function with bounded second derivative. We deal also with Fejer inequalities in cases that p, the weight function in Fejer inequality, is not symmetric but monotone on [a, b] .
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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
- 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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| 8. |
- Abylayeva, Akbota M., et al.
(författare)
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Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities
- 2018
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Ingår i: Mathematical Inequalities & Applications. - : Ele-math. - 1331-4343 .- 1848-9966. ; 21:1, s. 201-215
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Tidskriftsartikel (refereegranskat)abstract
- We establish criteria for both boundedness and compactness for some classes of integraloperators with logarithmic singularities in weighted Lebesgue spaces for cases 1 < p 6 q <¥ and 1 < q < p < ¥. As corollaries some corresponding new Hardy inequalities are pointedout.1
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| 9. |
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| 10. |
- Barza, Sorina, et al.
(författare)
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Sharp multidimensional multiplicative inequalities for weighted Lp spaces with homogeneous weights
- 1998
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 1:1, s. 53-67
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Tidskriftsartikel (refereegranskat)abstract
- Let Ω be an arbitrary cone in IRn with the origin as a vertex. A multidimensional multiplicative inequality for weighted Lp(Ω) -spaces with homogeneous weights is proved. The inequality is sharp and all cases of equality are pointed out. In particular, this inequality may be regarded as a weighted multidimensional extension of previous inequalities of Carlson, Beurling and Leviri.
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