Ostrowski Inequality

Irshad, Nazia; Khan, Asif R.; Mehmood, Faraz; Pečarić, Josip

doi:10.1007/978-3-030-90563-7_2

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2023

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“…Integral inequalities of the Ostrowski, Chebyshev, and Gruss type are well-known and appear in many areas of mathematics(for history and generalizations, see the renowned monograph [ 3 ], along with the papers [ 4 – 7 ]). Čebyšev and Ostrowski type inequalities, which have a very close relationship (see details in [ 8 ]), play an important role in many areas of mathematical applications and have received extensive attention from researchers.…”

Section: Introductionmentioning

confidence: 99%

Ostrowski and Čebyšev type inequalities for interval-valued functions and applications

Guo,

Zhu,

et al. 2023

PLoS ONE

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As an essential part of classical analysis, Ostrowski and Čebyšev type inequalities have recently attracted considerable attention. Due to its universality, the non-additive integral inequality takes several forms, including Sugeno integrals, Choquet integrals, and pseudo-integrals. Set-valued analysis, a well-known generalization of classical analysis, is frequently employed in studying mathematical economics, control theory, etc. Inspired by pioneering work on interval-valued inequalities, this paper establishes specific Ostrowski and Čebyšev type inequalities for interval-valued functions. Moreover, the error estimation to quadrature rules is presented as some applications for illustrating our results. In addition, illustrative examples are offered to demonstrate the applicability of the mathematical methods presented.

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Section: Introductionmentioning

confidence: 99%