Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 207-220.

GENERALIZED HARDY-TYPE INEQUALITY VIA LIDSTONE INTERPOLATING POLYNOMIAL AND NEW GREEN FUNCTIONS

Dora Pokaz

Abstract.   For a given general setting, involving measure spaces with positive σ-finite measures, we present new results regarding Hardy-type inequality. We established a connection between the difference operator obtained from Hardy-type inequality and the expression that includes Lidstone interpolating polynomial and four new Green functions. We discuss about 2n convexity of the function and consider the main result depending on the parity of the part of exponent and index n. Applying Hölder inequality for conjugate exponents p and q we get some consequential results. Finally, we derived bounds for the identity using Čebyšev functional and Ostrowski-type bound for the generalized Hardy's inequality.

2020 Mathematics Subject Classification.   26D10, 26D15, 39B62.

Key words and phrases.   Convex function, Hardy-type inequality, Lidstone interpolating polynomial, Green function, Čebyšev functional.

DOI: https://doi.org/10.21857/90836c2p8y

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