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Title: | Jensen and Chebyshev inequalities for interval-valued functions Nejednakosti Jensena i Čebiševa za intervalno-vrednosne funkcije |
Authors: | Medić Slavica | Keywords: | Semiring, -measure, pseudo-integral, Chebyshev inequality,Jensen inequality;poluprsten, -mera, pseudo-integral, nejednakost Čebiševa, nejednakost Jensena | Issue Date: | 25-Apr-2014 | Publisher: | Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu University of Novi Sad, Faculty of Technical Sciences at Novi Sad |
Abstract: | <p>Integralne nejednakosti Jensena i Čebiševa<br />uopštene su za integrale bazirane na neaditivnim<br />merama. Prvo uopštenje dokazano je za<br />pseudo-integral skupovno-vrednosne funkcije, a<br />drugo za pseudo-integral realno-vrednosne funkcije<br />u odnosu na intervalno-vrednosnu -meru.<br />Dokazana je i uopštena nejednakost Čebiševa<br />za pseudo-integral realno-vrednosne funkcije i<br />njena dva intervalno-vrednosna oblika. Nejednakost<br />Jensena je primenjena u principu premije, a<br />nejednakost Čebiševa na procenu verovatnoće.</p> <p>Integral inequalities of Jensen and Chebyshev type are<br />generalized for integrals based on nonadditive measures.<br />The first generalization is proven for the pseudointegral<br />of a set valued function and the second one<br />for the pseudo-integral of a real-valued function with<br />respect to the interval-valued -measure. Generalized<br />Chebyshev inequality for the pseudo-integral of a realvalued<br />function and its two interval-valued forms are<br />proven. Jensen inequality is applied in the premium<br />principle and Chebyshev inequality is applied to the<br />probability estimation.</p> |
URI: | https://open.uns.ac.rs/handle/123456789/28987 |
Appears in Collections: | FTN Teze/Theses |
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