Generalized Čebyšev and Grüss Type Results in Weighted Lebesgue Spaces

Saad Ihsan Butt, Josip Pečarić and Sanja Tipurić-Spužević ()
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Saad Ihsan Butt: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Punjab 54000, Pakistan
Josip Pečarić: Croatian Academy of Sciences and Arts, 10000 Zagreb, Croatia
Sanja Tipurić-Spužević: Faculty of Chemistry and Technology, University of Split, Rudera Boškovića 35, 21000 Split, Croatia

Mathematics, 2023, vol. 11, issue 7, 1-19

Abstract: 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 L ω Ω , 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 L ω p Ω , A , μ spaces. As an application, we provide several new bounds for Jensen–Grüss type differences.

Keywords: Sonin’s identity; Korkine’s identity; ?ebyšev functional; Grüss inequality; Jensen–Grüss inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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