| 51. |
- Abramovich, S., et al.
(författare)
-
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
-
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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| 52. |
- Abramovich, Shoshana, et al.
(författare)
-
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
-
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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| 53. |
- Abramovich, Shoshana, et al.
(författare)
-
Inequalities for averages of quasiconvex and superquadratic functions
- 2016
-
Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 19:2, s. 535-550
-
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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| 54. |
- Abramovich, Shoshana, et al.
(författare)
-
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
-
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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| 55. |
- Abramovich, Shoshana, et al.
(författare)
-
On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities
- 2015
-
Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 18:2, s. 615-627
-
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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| 56. |
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| 57. |
- Abramovich, Shoshana, et al.
(författare)
-
Some new estimates of the ‘Jensen gap’
- 2016
-
Ingår i: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X. ; 2016
-
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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| 58. |
- Abramovich, Shoshana, et al.
(författare)
-
Some new Hermite-Hadamard and Fejer type inequalities without convexity/concavity
- 2020
-
Ingår i: Mathematical Inequalities & Applications. - : Element. - 1331-4343 .- 1848-9966. ; 23:2, s. 447-458
-
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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| 59. |
- Abramovich, Shosana, et al.
(författare)
-
Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 3
- 2014
-
Ingår i: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. - Basel : Encyclopedia of Global Archaeology/Springer Verlag. - 9783034806473 - 9783034806480 ; , s. 1-10
-
Konferensbidrag (refereegranskat)abstract
- For usual Hardy type inequalities the natural “breaking point” (the parameter value where the inequality reverses) is p = 1. Recently, J. Oguntuase and L.-E. Persson proved a refined Hardy type inequality with breaking point at p = 2. In this paper we show that this refinement is not unique and can be replaced by another refined Hardy type inequality with breaking point at p = 2. Moreover, a new refined Hardy type inequality with breaking point at p = 3 is obtained. One key idea is to prove some new Jensen type inequalities related to convex or superquadratic funcions, which are also of independent interest
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| 60. |
- Abramovich, Shoshana, et al.
(författare)
-
Some new refined Hardy type inequalities with general kernels and measures
- 2010
-
Ingår i: Aequationes Mathematicae. - : Springer Science and Business Media LLC. - 0001-9054 .- 1420-8903. ; 79:1-2, s. 157-172
-
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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