Generalization of the Stolarsky type inequality for pseudo-integrals

Daraby, Bayaz

doi:10.1016/j.fss.2011.08.005

Cited by 12 publications

(8 citation statements)

References 23 publications

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“…Some of these generalizations posses their own Bushell-Okrasiński type inequalities. For instance, pseudo-integrals for which, loosely speaking, instead of the field of real numbers one considers a semi-ring defined on a real interval, exhibit a version of (14) with redefined multiplication and addition [12]. Notice how different various properties of these integrals might be from the Lebesgue case (like the loss of linearity).…”

Section: Reversed Jensen Type Inequalitiesmentioning

confidence: 99%

The Bushell-Okrasiński inequality

Płociniczak¹

2022

Preprint

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We present an expository account of the Bushell-Okrasiński inequality, the motivation behind it, its history, and several generalizations. This inequality originally appeared in studies of nonlinear Volterra equations but very soon gained interest of its own. The basic result has quickly been generalized and extended in different directions strengthening the assertion, generalizing the kernel and nonlinearity, providing the optimal prefactor, finding conditions under which it becomes an equality, and formulating variations valid for other than Lebesgue integrals. We review all of these aspects.

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Section: Reversed Jensen Type Inequalitiesmentioning

confidence: 99%

The Bushell-Okrasiński inequality

Płociniczak¹

2022

Preprint

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“…Daraby et. al.,in [3,4,5,6,7] studied and generalized some other inequalities for the Fuzzy and Pseudo integrals, for example, he stated and proved [2] the Stolarsky type of inequality for Pseudo integrals as it follows:…”

Section: Introductionmentioning

confidence: 99%

Diaz-Metcalf Type Inequality for Sugeno and Pseudo Integrals

Karimzadeha¹,

Darabyb²,

Rahimic³

2022

Preprint

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“…Chebyshev type inequalities for pseudo-integrals were investigated in [42] and Chebyshev's inequality for Choquet-like integral was subsequently introduced in [43]. Daraby [44] obtained generalization of the Stolarsky type inequality for pseudo-integrals. Li et al [45] investigated generalization of the Lyapunov type inequality for pseudo-integrals.…”

Section: Introductionmentioning

confidence: 99%

Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures

Xie

Gong

2019

Journal of Function Spaces

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The aim of this paper is to generalize the Choquet-like integral with respect to a nonmonotonic fuzzy measure for generalized real-valued functions and set-valued functions, which is based on the generalized pseudo-operations and σ-⊕-measures. Furthermore, the characterization theorem and transformation theorem for the integral are given. Finally, we study the Lyapunov type inequality and Stolarsky type inequality for the Choquet-like integral.

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Generalization of the Stolarsky type inequality for pseudo-integrals

Cited by 12 publications

References 23 publications

The Bushell-Okrasiński inequality

The Bushell-Okrasiński inequality

Diaz-Metcalf Type Inequality for Sugeno and Pseudo Integrals

Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures

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