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The Pečarić Journal of Mathematical Inequalities (PJMI)

ISSN: xxxx-xxxx (Online) xxxx-xxxx (Print)
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  • Research article

On a linear transformation of the Cauchy and related inequalities

Julije Jakšetić1, Dragana Kordić2, Josip Pečarić3, Lars Erik Persson4,5
1University of Zagreb Faculty of Food Technology and Biotechnology, Mathematics department, Pierottijeva 6, 10000 Zagreb, Croatia
2University of Mostar, Faculty of Mechanical Engineering, Computing and Electrical Engineering, Matice hrvatske bb, 88000 Mostar, Bosnia and Herzegovina
3Croatian Academy of Sciences and Arts, Trg Nikole Šubi´ca Zrinskog 11, 10000 Zagreb, Croatia
4UiT The Arctic University of Norway P. O. Box 385, Narvik N-8505 Norway
5Department of Mathematics, Uppsala University Box 480751 06, Uppsala, Sweden
Copyright © Julije Jakšetić, Dragana Kordić, Josip Pečarić, Lars Erik Persson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • Received: 02/03/2025
  • Accepted: 15/07/2025
  • Published: 20/09/2025

Abstract

By examining the properties of a certain linear transformation of functionals, we present applications of Cauchy, Aczel, Callebaut, and Beckenbach type inequalities. Additionally, we provide results for complex functionals.

Keywords: Cauchy inequality, Callebaut inequality, Aczel inequality, Beckenbach inequality, Hölder’s inequality