Article ID: MTJPAM-D-23-00022

Title: Hardy-type inequalities generalized via Montgomery identity


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-23-00022; Volume 6 / Issue 3 / Year 2024, Pages 62-71

Document Type: Research Paper

Author(s): ‪Kristina Krulić Himmelreich a , Josip Pečarić b , Dora Pokaz c , Marjan Praljak d

aUniversity of Zagreb Faculty of Textile Technology, Prilaz Baruna Filipovića 28a, 10000 Zagreb, Croatia

bCroatian Academy of Sciences and Arts, Trg Nikole Šubića Zrinskog 11, 10000 Zagreb, Croatia

cUniversity of Zagreb Faculty of Civil Engineering, Fra Andrije Kačića Miošića 26, 10000 Zagreb, Croatia

dUniversity of Zagreb Faculty of Food Technology and Biotechnology, Pierrottijeva 6, 10000 Zagreb, Croatia

Received: 4 September 2023, Accepted: 23 September 2023, Published: 7 November 2023

Corresponding Author: Dora Pokaz (Email address: dora.pokaz@grad.unizg.hr)

Full Text: PDF

Abstract

In this paper, we give generalization of Hardy’s type inequalities by using the Green function and the Montgomery identity. We lean on the idea of the generalization of the Hardy inequality that includes measure spaces with positive σ-finite measures. We provide the result concerning the n-convexity property of the function and establish the connection between new and known result. In order to get upper bounds for the identities related to generalizations of the Hardy’s inequality, we obtain Grüss and Ostrowski-type inequalities.

Keywords: Inequalities, Hardy type inequalities, Green function, Chebyshev functional, Montgomery identity, convex function, kernel

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