Reverse Hölder inequality and Fibonacci numbers
DOI :
https://doi.org/10.5269/bspm.76681Résumé
In this paper we present reverse Hölder-type inequalities with power sums . We apply these results to sums involving Fibonacci numbers.
Références
[1] H. Alzer, F. Luca, An inequality for the Fibonacci numbers, Math. Bohem. 147, 587-590, (2022).
[2] H. Alzer, M. K. Kwong, Extension of an Inequality for Fibonacci Numbers, Integers 22, Paper No. A85, (2022).
[3] A. Dujella, J. Jakšetic, J. Pecaric, Fibonacci numbers and Hölder inequality , Bull. Transilv. Univ. Brasov Ser. III, to appear.
[4] R. P. Grimaldi, Fibonacci and Catalan numbers, John Wiley & Sons, Inc., Hoboken, NJ, (2012).
[5] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd ed. Cambridge Univ. Press, (1934).
[6] D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic, Dordrecht, (1993).
[7] M. Nagy, S. R. Cowell, V. Beiu, Survey of Cubic Fibonacci Identities When Cuboids Carry Weight, International Journal of Computers Communications & Control, 17(2), (2022).
[8] H. Ohtsuka, S. Nakamura, A new formula for the sum of the sixth powers of Fibonacci numbers, Congressus Numerantium, Proceedings of the thirteenth conference on Fibonacci numbers and their applications 201, 297—300, (2010).
[9] P. G. Popescu, J. L. Díaz-Barrero, Certain inequalities for convex functions, J. Inequal. Pure Appl. Math. 7(2), Article 41, (2006).
[10] K. G. Recke, Problem B - 153, The Fibonacci Quarterly, 7(3) (1969).
[11] W. T. Sulaiman, Reverses of Minkowski’s, Hölder’s, and Hardy’s Integral Inequalities, International Journal of Modern Mathematical Sciences, 1(1), 14–24, (2012).
[2] H. Alzer, M. K. Kwong, Extension of an Inequality for Fibonacci Numbers, Integers 22, Paper No. A85, (2022).
[3] A. Dujella, J. Jakšetic, J. Pecaric, Fibonacci numbers and Hölder inequality , Bull. Transilv. Univ. Brasov Ser. III, to appear.
[4] R. P. Grimaldi, Fibonacci and Catalan numbers, John Wiley & Sons, Inc., Hoboken, NJ, (2012).
[5] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd ed. Cambridge Univ. Press, (1934).
[6] D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic, Dordrecht, (1993).
[7] M. Nagy, S. R. Cowell, V. Beiu, Survey of Cubic Fibonacci Identities When Cuboids Carry Weight, International Journal of Computers Communications & Control, 17(2), (2022).
[8] H. Ohtsuka, S. Nakamura, A new formula for the sum of the sixth powers of Fibonacci numbers, Congressus Numerantium, Proceedings of the thirteenth conference on Fibonacci numbers and their applications 201, 297—300, (2010).
[9] P. G. Popescu, J. L. Díaz-Barrero, Certain inequalities for convex functions, J. Inequal. Pure Appl. Math. 7(2), Article 41, (2006).
[10] K. G. Recke, Problem B - 153, The Fibonacci Quarterly, 7(3) (1969).
[11] W. T. Sulaiman, Reverses of Minkowski’s, Hölder’s, and Hardy’s Integral Inequalities, International Journal of Modern Mathematical Sciences, 1(1), 14–24, (2012).
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Publié
2025-09-18
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Research Articles
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