| 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. |
- Nikolova, Ludmila, et al.
(författare)
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A new look at classical inequalities involving Banach lattice norms
- 2017
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2017
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Tidskriftsartikel (refereegranskat)abstract
- Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by discussing some results of this type and also by deriving some new results related to classical Popoviciu’s, Bellman’s and Beckenbach-Dresher’s inequalities.
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| 3. |
- Nikolova, Ludmila, et al.
(författare)
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Continuous refinements of some Jensen-type inequalities via strong convexity with applications
- 2022
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2022:1
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we prove new continuous refinements of some Jensen type inequalities in both direct and reversed forms. As applications we also derive some continuous refinements of Hermite-Hadamard, Holder, and Popoviciu type inequalities. As particular cases we point out the corresponding results for sums and integrals showing that our results contain both several well-known but also some new results for these special cases.
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| 4. |
- Nikolova, Ljudmila I., et al.
(författare)
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Continuous Forms of Classical Inequalities
- 2016
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Ingår i: Mediterranean Journal of Mathematics. - : Springer Science and Business Media LLC. - 1660-5446 .- 1660-5454. ; 13:5, s. 3483-3497
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Tidskriftsartikel (refereegranskat)abstract
- The main aim of this paper is to focus on the question to develop classical inequalities to hold in a more general “continuous” form (involving infinitely many functions and/or spaces). First, we discuss such developments concerning Hölder’s and Minkowski’s inequalities. After that we present such new general developments of Popoviciu’s and Bellman’s inequalities. Finally, we present some applications, possible extensions and questions for further research.
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| 5. |
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| 6. |
- Nikolova, Ludmila, et al.
(författare)
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Refinements of some classical inequalities via superquadraticity
- 2022
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2022:1
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Tidskriftsartikel (refereegranskat)abstract
- Some new refined versions of the Jensen, Minkowski, and Hardy inequalities are stated and proved. In particular, these results both generalize and unify several results of this type. Some results are also new for the classical situation.
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| 7. |
- Nikolova, Ludmila, et al.
(författare)
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Some new refinements of the Young, Hölder, and Minkowski inequalities
- 2023
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2023:1
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Tidskriftsartikel (refereegranskat)abstract
- We prove and discuss some new refined Hölder inequalities for any p> 1 and also a reversed version for 0 < p< 1. The key is to use the concepts of superquadraticity, strong convexity, and to first prove the corresponding refinements of the Young and reversed Young inequalities. Refinements of the Minkowski and reversed Minkowski inequalities are also given.
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| 8. |
- Nikolova, Ludmila, et al.
(författare)
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The Beckenbach-Dresher inequality in the psi-direct sums of spaces and related results
- 2012
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 2012:1
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Tidskriftsartikel (refereegranskat)abstract
- Let ~ A : [0; 1] ! R be a concave function with ~ A(0) = ~ A(1) = 1. There is a corresponding map k:k ~ A for which the inverse Minkowski inequality holds. Several properties of that map are obtained. Also, we consider the Beckenbach{Dresher type inequality connected with A-direct sums of Banach spaces and of ordered spaces. In the last section we investigate the properties of functions A!;q and k:k!;q , (0 < ! < 1; q < 1) related to the Lorentz sequence space. Other posibilities for parameters ! and q are considered, the inverse HAolder inequalities and more variants of the Beckenbach{Dresher inequalities are obtained.
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