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Search Results (3)

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Keywords = interval valued (set) multifunction

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12 pages, 275 KB  
Article
Inequalities in Riemann–Lebesgue Integrability
by Anca Croitoru, Alina Gavriluţ, Alina Iosif and Anna Rita Sambucini
Mathematics 2024, 12(1), 49; https://doi.org/10.3390/math12010049 - 22 Dec 2023
Cited by 3 | Viewed by 2013
Abstract
In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multivalued case, [...] Read more.
In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multivalued case, in particular for Riemann–Lebesgue integrable interval-valued multifunctions, and obtain some inequalities, such as a Minkowski-type inequality, a Beckenbach-type inequality and some generalizations of Hölder inequalities. Full article
15 pages, 333 KB  
Article
Convergence Theorems in Interval-Valued Riemann–Lebesgue Integrability
by Anca Croitoru, Alina Gavriluţ, Alina Iosif and Anna Rita Sambucini
Mathematics 2022, 10(3), 450; https://doi.org/10.3390/math10030450 - 30 Jan 2022
Cited by 11 | Viewed by 3087
Abstract
We provide some limit theorems for sequences of Riemann–Lebesgue integrable functions. More precisely, Lebesgue-type convergence and Fatou theorems are established. Then, these results are extended to the case of Riemann–Lebesgue integrable interval-valued multifunctions. Full article
17 pages, 1407 KB  
Article
The Riemann-Lebesgue Integral of Interval-Valued Multifunctions
by Danilo Costarelli, Anca Croitoru, Alina Gavriluţ, Alina Iosif and Anna Rita Sambucini
Mathematics 2020, 8(12), 2250; https://doi.org/10.3390/math8122250 - 20 Dec 2020
Cited by 16 | Viewed by 3767
Abstract
We study Riemann-Lebesgue integrability for interval-valued multifunctions relative to an interval-valued set multifunction. Some classic properties of the RL integral, such as monotonicity, order continuity, bounded variation, convergence are obtained. An application of interval-valued multifunctions to image processing is given for the [...] Read more.
We study Riemann-Lebesgue integrability for interval-valued multifunctions relative to an interval-valued set multifunction. Some classic properties of the RL integral, such as monotonicity, order continuity, bounded variation, convergence are obtained. An application of interval-valued multifunctions to image processing is given for the purpose of illustration; an example is given in case of fractal image coding for image compression, and for edge detection algorithm. In these contexts, the image modelization as an interval valued multifunction is crucial since allows to take into account the presence of quantization errors (such as the so-called round-off error) in the discretization process of a real world analogue visual signal into a digital discrete one. Full article
(This article belongs to the Special Issue Set-Valued Analysis)
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