Generalizations of Hardy type inequalities by Taylor's formula

Kristina Krulić Himmelreich

doi:10.1515/ms-2022-0005

Authors

Kristina Krulić Himmelreich University of Zagreb

DOI:

https://doi.org/10.1515/ms-2022-0005

Keywords:

Inequalities, Hardy type inequalities, Green function, Taylor interpolating polynomial, Chebyshev functional, convex function, kernel, exponentially convex functions, log-convex functions, means

Abstract

In this paper we use Taylor's formula to prove new Hardy-type inequalities involving convex functions. We give new results that involve the Hardy–Hilbert inequality, Pólya-Knopp inequality and bounds for the identity related to the Hardy-type functional. At the end, mean value theorems of Cauchy type are given.

Author Biography

Kristina Krulić Himmelreich, University of Zagreb

University of Zagreb Faculty of Textile and Technology
Prilaz baruna Filipovica 28a
10000 Zagreb
CROATIA