| 1. |
- Abramovich, S., et al.
(author)
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Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities
- 2018
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In: Mathematical Inequalities & Applications. - : Element D.O.O.. - 1331-4343 .- 1848-9966. ; 21:3, s. 759-772
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Journal article (peer-reviewed)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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| 2. |
- Abramovich, Shoshana, et al.
(author)
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Inequalities for averages of quasiconvex and superquadratic functions
- 2016
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In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 19:2, s. 535-550
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Journal article (peer-reviewed)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.
(author)
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On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities
- 2015
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In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 18:2, s. 615-627
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Journal article (peer-reviewed)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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| 4. |
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| 5. |
- Abylayeva, Akbota M., et al.
(author)
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Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities
- 2018
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In: Mathematical Inequalities & Applications. - : Ele-math. - 1331-4343 .- 1848-9966. ; 21:1, s. 201-215
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Journal article (peer-reviewed)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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| 6. |
- Aljinovic, Andrea Aglic, et al.
(author)
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Josip Pecaric- and his life in mathematics and politics
- 2019
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In: Mathematical Inequalities & Applications. - : Element. - 1331-4343 .- 1848-9966. ; 22:4, s. 1067-1080
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Journal article (peer-reviewed)abstract
- It is impossible in limited number of pages to give a fair picture of such a remarkable man, great mathematician and human being as Josip Pecaric. Our intention is instead to complement the picture of him in various ways. We hope that our paper will give also someflavor of Josip as family man, fighter, supervisor,international authority, author (also in other subjects than mathematics), fan of the Croatian football team, and not only as his obvious role as our King of Inequalities.
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| 7. |
- Baǐarystanov, Askar O., et al.
(author)
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Some new hardy-type inequalities in q-analysis
- 2016
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In: Journal of Mathematical Inequalities. - : Element d.o.o.. - 1846-579X .- 1848-9575. ; 10:3, s. 761-781
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Journal article (peer-reviewed)abstract
- We derive necessary and sufficient conditions (of Muckenhoupt-Bradley type) for the validity of q-analogs of (r, p)-weighted Hardy-type inequalities for all possible positive values of the parameters r and p. We also point out some possibilities to further develop the theory of Hardy-type inequalities in this new direction
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| 8. |
- Burtseva, Evgeniya, 1988-, et al.
(author)
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Multi–dimensional Hardy type inequalities in Hölder spaces
- 2018
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In: Journal of Mathematical Inequalities. - Zagreb : Element D.O.O.. - 1846-579X .- 1848-9575. ; 12:3, s. 719-729
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Journal article (peer-reviewed)abstract
- Most Hardy type inequalities concern boundedness of the Hardy type operators in Lebesgue spaces. In this paper we prove some new multi-dimensional Hardy type inequalities in Hölder spaces.
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| 9. |
- Fabelurin, O.O, et al.
(author)
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Multidimensional Hardy-type inequalities on time scales with variable exponents
- 2019
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In: Journal of Mathematical Inequalities. - Zagreb, Croatia : Element. - 1846-579X .- 1848-9575. ; 13:3, s. 725-736
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Journal article (peer-reviewed)abstract
- A new Jensen inequality for multivariate superquadratic functions is derived and proved. The derived Jensen inequality is then employed to obtain the general Hardy-type integral inequality for superquadratic and subquadratic functions of several variables.
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| 10. |
- Kanjilal, Saikat, et al.
(author)
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Equivalent Integral Conditions Related to Bilinear Hardy-type Inequalities
- 2019
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In: Mathematical Inequalities & Applications. - : Element. - 1331-4343 .- 1848-9966. ; 22:4, s. 1535-1548
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Journal article (peer-reviewed)abstract
- Infinitely many, even scales of, equivalent conditions are derived to characterize the bilinear Hardy-type inequality under various ranges of parameters.
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