Generalizations of Hardy type inequalities by Taylor's formula

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

Published

2022-02-16

Issue

Vol. 72 No. 1 (2022): Mathematica Slovaca

Section

Articles - Other topics