Monotonicity character of convex combinations of two sequences generated by the square of the cube root function
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Date
2025-10-15
Authors
Stevic, Stevo
Iričanin, Bratislav D.
Kosmala, Witold
Šmarda, Zdeněk
0000-0002-7202-9764Advisor
Referee
Mark
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Abstract
There is a natural connection between the finite sums of the reciprocals of the squares of the cube roots of positive natural numbers and two definite integrals. By using the differences between the sums and the integrals are formed in a natural way two sequences of real numbers converging to the same finite limit. We completely determine the monotonicity character of the sequences which are obtained by convex combinations of the two sequences, in an elegant way. We also present an interesting result about monotonicity character of a real function on the interval , which is used in the proof of the main result. The results are important for solving difference equations.
There is a natural connection between the finite sums of the reciprocals of the squares of the cube roots of positive natural numbers and two definite integrals. By using the differences between the sums and the integrals are formed in a natural way two sequences of real numbers converging to the same finite limit. We completely determine the monotonicity character of the sequences which are obtained by convex combinations of the two sequences, in an elegant way. We also present an interesting result about monotonicity character of a real function on the interval , which is used in the proof of the main result. The results are important for solving difference equations.
There is a natural connection between the finite sums of the reciprocals of the squares of the cube roots of positive natural numbers and two definite integrals. By using the differences between the sums and the integrals are formed in a natural way two sequences of real numbers converging to the same finite limit. We completely determine the monotonicity character of the sequences which are obtained by convex combinations of the two sequences, in an elegant way. We also present an interesting result about monotonicity character of a real function on the interval , which is used in the proof of the main result. The results are important for solving difference equations.
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Citation
Journal of Inequalities and Applications. 2025, vol. 2025, issue 122, 12 p.
https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-025-03375-7
https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-025-03375-7
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Peer-reviewed
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en
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
http://creativecommons.org/licenses/by-nc-nd/4.0/