On Some Inequalities with Fibonacci Numbers via Weighted Reverse Hölder Inequalities

Anamarija Perušić Pribanić

doi:10.2478/amsil-2026-0007

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On Some Inequalities with Fibonacci Numbers via Weighted Reverse Hölder Inequalities

Annales Mathematicae Silesianae

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By: Anamarija Perušić Pribanić

Open Access

|Apr 2026

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.

References

A. Dujella, J. Jakšetić, and J. Pečarić, Fibonacci numbers and Hölder inequality, Bull. Transilv. Univ. Braşov Ser. III, to appear.
Search in Google Scholar Back to article
R.P. Grimaldi, Fibonacci and Catalan Numbers, John Wiley & Sons, Inc., Hoboken, NJ, 2012.
Search in Google Scholar Back to article
G.H. Hardy, J.E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge University Press, London, 1934.
Search in Google Scholar Back to article
R.S. Melham, Closed forms for finite sums of weighted products of generalized Fibonacci numbers, Fibonacci Quart. 55 (2017), no. 2, 99–104.
Search in Google Scholar Back to article
D.S. Mitrinović, J.E. Pečarić, and A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers Group, Dordrecht, 1993.
Search in Google Scholar Back to article
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.
Open DOI Search in Google Scholar Back to article
H. Ohtsuka and S. Nakamura, A new formula for the sum of the sixth powers of Fibonacci numbers, in: F. Luca and P. 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.
Search in Google Scholar Back to article
A. Perušić Pribanić, Reverse Hölder inequality and Fibonacci numbers, Bol. Soc. Paran. Mat. 43 (2025), 9 pp.
Search in Google Scholar Back to article
P. Stănică, Generating functions, weighted and non-weighted sums for powers of second-order recurrence sequences, Fibonacci Quart. 41 (2003), no. 4, 321–333.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/amsil-2026-0007 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Submitted on: Sep 19, 2025

Accepted on: Mar 23, 2026

Published on: Apr 17, 2026

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Fibonacci sequence,

Fibonacci identity,

weighted power sum,

reverse Hölder inequality

Related subjects:

Mathematics,

General mathematics

© 2026 Anamarija Perušić Pribanić, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

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