Extended Jensen's functional for diamond integral via Hermite polynomial (Q1981849)
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scientific article; zbMATH DE number 7391743
| Language | Label | Description | Also known as |
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| English | Extended Jensen's functional for diamond integral via Hermite polynomial |
scientific article; zbMATH DE number 7391743 |
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Extended Jensen's functional for diamond integral via Hermite polynomial (English)
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7 September 2021
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Summary: In this paper, with the help of Hermite interpolating polynomial, extension of Jensen's functional for \(n\)-convex function is deduced from Jensen's inequality involving diamond integrals. Special Hermite conditions, including Taylor two-point formula and Lagrange's interpolation, are also deployed to find further extensions of Jensen's functional. The paper also includes discussion on bounds for Grüss-type inequality, Ostrowski-type inequality, and Chebyshev functional associated with newly defined Jensen's functional.
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