Liapounoff type inequality for pseudo-integral of interval-valued function

Tatjana Grbić; Slavica Medić; Nataša Duraković; Sandra Buhmiler; Slaviša Dumnić; Janja Jerebic; Tatjana Grbić; Slavica Medić; Nataša Duraković; Sandra Buhmiler; Slaviša Dumnić; Janja Jerebic

doi:10.3934/math.2022302

AIMS Mathematics

2022, Volume 7, Issue 4: 5444-5462. doi: 10.3934/math.2022302

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Research article

Liapounoff type inequality for pseudo-integral of interval-valued function

1.
Faculty of Technical Sciences, University of Novi Sad, Novi Sad 21000, Serbia
2.
Faculty of Organizational Sciences, University of Maribor, Kranj 6230, Slovenia

Received: 27 September 2021 Revised: 13 December 2021 Accepted: 13 December 2021 Published: 07 January 2022
MSC : 28A25, 28B20, 54C60

In this paper, two new Liapounoff type inequalities in terms of pseudo-analysis dealing with set-valued functions are given. The first one is given for a pseudo-integral of set-valued function where pseudo-operations are given by a generator $ g:[0, \infty]\to [0, \infty] $ and the second one is given for the semiring $ ([0, \infty], \sup, \odot) $ with generated pseudo-multiplication. The interval Liapounoff inequality is applied for estimation of interval-valued central $ g $-moment of order $ n $ for interval-valued functions in a $ g $-semiring.
Citation: Tatjana Grbić, Slavica Medić, Nataša Duraković, Sandra Buhmiler, Slaviša Dumnić, Janja Jerebic. Liapounoff type inequality for pseudo-integral of interval-valued function[J]. AIMS Mathematics, 2022, 7(4): 5444-5462. doi: 10.3934/math.2022302

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Abstract

In this paper, two new Liapounoff type inequalities in terms of pseudo-analysis dealing with set-valued functions are given. The first one is given for a pseudo-integral of set-valued function where pseudo-operations are given by a generator $ g:[0, \infty]\to [0, \infty] $ and the second one is given for the semiring $ ([0, \infty], \sup, \odot) $ with generated pseudo-multiplication. The interval Liapounoff inequality is applied for estimation of interval-valued central $ g $-moment of order $ n $ for interval-valued functions in a $ g $-semiring.

References

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