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This article is cited in 2 scientific papers (total in 2 papers)
Refinement of continuous forms of classical inequalities
L. Nikolovaa, L.-E. Perssonbc, S. Varošanecd a Department of Mathematics and Informatics,
Sofia University
Sofia,
Bulgaria
b Department of Mathematics and Computer Science,
Karlstad University,
Karlstad,
Sweden
c Department of Computer Science and Computational Engeniering,
UiT, The Artic University of Norway, Narvik, Norway
d Department of Mathematics,
University of Zagreb,
Zagreb,
Croatia
Abstract:
In this article we give refinements of the continuous forms of some classical inequalities i.e. of the inequalities which involve infinitely many functions instead of finitely many. We present new general results for such inequalities of Hölder-type and of Minkowski-type as well as for their reverses known as Popoviciu- and Bellman-type inequalities. Properties for related functionals are also established. As particular cases of these results we derive both well-known and new refinements of the corresponding classical inequalities for integrals and sums
Keywords and phrases:
inequalities, Hölder-, Minkowski-, Popoviciu- and Bellman-type inequalities, continuous forms, measure spaces, related functionals.
Received: 27.11.2020
Citation:
L. Nikolova, L.-E. Persson, S. Varošanec, “Refinement of continuous forms of classical inequalities”, Eurasian Math. J., 12:2 (2021), 59–73
Linking options:
https://www.mathnet.ru/eng/emj404 https://www.mathnet.ru/eng/emj/v12/i2/p59
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