Weighted quadrature rules via Grüss type inequalities for weighted Lp spaces

Aljinović, Andrea Aglić; Pečarić, Josip; Tipurić-Spužević, Sanja

doi:10.1016/j.amc.2015.04.005

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Theorem 2 Consider the Functions1

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2023

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“…Later, in [22], Aljinović et al provided new weighted estimates of the Grüss inequality with the bounding functions in weighted L p ω, [u,vs. ] spaces by considering uniform weight functions.…”

Section: Theorem 2 Consider the Functionsmentioning

confidence: 99%

Generalized Čebyšev and Grüss Type Results in Weighted Lebesgue Spaces

2023

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The classical Grüss and related inequalities have spurred a range of improvements, refinements, generalizations, and extensions. In the present article, we provide generalizations of Sokolov’s inequality in weighted Lebesgue LωΩ,A,μ spaces by employing the weighted Sonin’s identity and Čebyšev functional. As a result, we provide a generalized Grüss inequality in which the bounding constants are improved with bounding functions in LωpΩ,A,μ spaces. As an application, we provide several new bounds for Jensen–Grüss type differences.

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Section: Theorem 2 Consider the Functionsmentioning

confidence: 99%