Extended Jensen’s functional for diamond integral via Green’s function and Hermite polynomial

In this paper, with the help of Green’s function and Hermite interpolating polynomial, an extension of Jensen’s functional for n -convex functions is deduced from Jensen’s inequality involving diamond integrals. Special Hermite conditions, including Taylor two point formula and Lagrange’s interpolat...

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Bibliographic Details
Published in:Journal of inequalities and applications 2022-04, Vol.2022 (1), p.1-15, Article 50
Main Authors: Bibi, Fazilat, Bibi, Rabia, Nosheen, Ammara, Pečarić, Josip
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Diamond integrals
Diamonds
Functionals
Green's functions
Green’s function
Hermite polynomial
Hermite polynomials
Inequality
Interpolation
Jensen’s inequality
Mathematical analysis
Mathematics
Mathematics and Statistics
Time scales
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Summary:In this paper, with the help of Green’s function and Hermite interpolating polynomial, an extension of Jensen’s functional for n -convex functions 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 the further extensions of Jensen’s functional. This paper also includes discussion on bounds for Grüss inequality, Ostrowski inequality, and Čebyšev functional associated to the newly defined Jensen’s functional.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-022-02785-1