Inequality of Hardy–type for n–convex function via interpolation polynomial and Green functions

Scientific paper - Original scientific paper

• Author: Dora Pokaz
• Author's institution: University of Zagreb; Faculty of Civil Engineering
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract (english)

We obtain new results on the Hardy-type inequality in the general context, in terms of measure spaces with positive σ -finite measures. The connection is made between the difference operator derived from the Hardy-type inequality on the one hand and the expression containing the interpolating polynomial of Abel-Gontscharoff and the four Green functions on the other hand. We discuss the n-convexity of the function and consider the result depending on the parity of the indexes n and m. Further results are obtained by using the Holder inequality for conjugate exponents p and q . Finally, we derive upper bounds for the remainder, obtained from the main result, using the Čebyšev functional. The Ostrowski-type bound for the generalized Hardy inequality is also given.

• Keywords (english): convex function; Hardy-type inequality; Abel-Gontscharoff interpolating polynomial; Green function; Čebyšev functional.
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Mathematical inequalities & applications
• Numbering: vol. -, no. -, p. -, -
• e-ISSN: 1848-9966
• URN:NBN: urn:nbn:hr:237:088295
• Publication: 2023
• Type of resource: Text
• Access conditions: Open access
• Created on: 2024-09-05 08:55:00