On some inequalities with Fibonacci numbers via weighted reverse Hölder inequalities

Anamarija Perušić Pribanić

Published: 2026-04-17

2025

On some inequalities with Fibonacci numbers via weighted reverse Hölder inequalities

Anamarija Perušić Pribanić

Abstract

In this paper, we introduce new inequalities for weighted sums of powers. By utilizing known Fibonacci identities alongside our generalized inequalities, we derive new sequences of inequalities for Fibonacci numbers.

Keywords:

Fibonacci sequence , Fibonacci identity , weighted power sum , reverse Hölder inequality

Download files

PDF

Citation rules

Perušić Pribanić, A. (2026). On some inequalities with Fibonacci numbers via weighted reverse Hölder inequalities. Annales Mathematicae Silesianae. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/22230

Licence

This work is licensed under a Creative Commons Attribution 4.0 International License.

The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.

Similar Articles

Ludwig Reich, Families of commuting formal power series, semicanonical forms and iterative roots , Annales Mathematicae Silesianae: Vol. 8 (1994)
Göksal Bilgici, Tuncay Deniz Şentürk, Some addition formulas for Fibonacci, Pell and Jacobsthal numbers , Annales Mathematicae Silesianae: Vol. 33 (2019)
Marta Nowakowska, Algebraic properties of semi-direct sums of rings , Annales Mathematicae Silesianae: Vol. 39 No. 2 (2025)
Cristian Conde, Refinements of the Hermite–Hadamard inequality in NPC global spaces , Annales Mathematicae Silesianae: Vol. 32 (2018)
Tomasz Łukasz Żynda, Reproducing kernels of weight square-summable sequences Hilbert spaces , Annales Mathematicae Silesianae: Vol. 33 (2019)
Magdalena Chmara, A generalized version of the Lions-type lemma , Annales Mathematicae Silesianae: Vol. 37 No. 2 (2023)
Árpád Száz, A Lagrange-type increment inequality , Annales Mathematicae Silesianae: Vol. 10 (1996)
Karol Baron, Remarks connected with the weak limit of iterates of some random-valued functions and iterative functional equations , Annales Mathematicae Silesianae: Vol. 34 No. 1 (2020)
Teodoro Lara, Nelson Merentes, Edgar Rosales, Ambrosio Tineo, Properties and characterizations of convex functions on time scales , Annales Mathematicae Silesianae: Vol. 32 (2018)
Amir Hosein Mokhtari, Fahimeh Moafian, Hamid Reza Ebrahimi Vishki, Lie derivations on trivial extension algebras , Annales Mathematicae Silesianae: Vol. 31 (2017)

<< < 1 2 3 4 5 6 7 8 9 10 > >>

You may also start an advanced similarity search for this article.

References

A. Dujella, J. Jakšetić, and J. Pečarić, Fibonacci numbers and Hölder inequality, Bull. Transilv. Univ. Braşov Ser. III, to appear.
Google Scholar

R.P. Grimaldi, Fibonacci and Catalan Numbers, John Wiley & Sons, Inc., Hoboken, NJ, 2012.
Google Scholar

G.H. Hardy, J.E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge University Press, London, 1934.
Google Scholar

R.S. Melham, Closed forms for finite sums of weighted products of generalized Fibonacci numbers, Fibonacci Quart. 55 (2017), no. 2, 99–104.
Google Scholar

D.S. Mitrinović, J.E. Pečarić, and A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers Group, Dordrecht, 1993.
Google Scholar

M. Nagy, S.R. Cowell, and V. Beiu, Survey of cubic Fibonacci identities when cuboids carry weight, Int. J. Comput. Commun. Control 17 (2022), no. 2, Art. No. 4616, 20 pp. DOI: 10.15837/ijccc.2022.2.461.
Google Scholar

H. Ohtsuka and S. Nakamura, A new formula for the sum of the sixth powers of Fibonacci numbers, in: F. Luca and Stănică (eds.), Proceedings of the 13th International Conference on Fibonacci Numbers and Their Applications, Patras, Greece, July 7–11, 2008, Congr. Numer. 201 (2010), pp. 297–300.
Google Scholar

A. Perušić Pribanić, Reverse Hölder inequality and Fibonacci numbers, Bol. Soc. Paran. Mat. 43 (2025), 9 pp.
Google Scholar

P. Stănică, Generating functions, weighted and non-weighted sums for powers of second-order recurrence sequences, Fibonacci Quart. 41 (2003), no. 4, 321–333.
Google Scholar

W.T. Sulaiman, Reverses of Minkowski’s, Hölder’s, and Hardy’s integral inequalities, Int. J. Mod. Math. Sci. 1 (2012), no. 1, 14–24.
Google Scholar

2025
Published: 2025-11-02

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

Licence CC

This work is licensed under a Creative Commons Attribution 4.0 International License.

Submit