Monotonicity character of convex combinations of two sequences generated by the square of the cube root function
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 $[1,+\infty )$ , which is used in the proof of the main result.
Authors
- Stevo Stević (ORCID: https://orcid.org/0000-0002-7202-9764)
- Zdenĕk Šmarda (ORCID: https://orcid.org/0000-0002-9559-6630)
- Bratislav Iričanin (ORCID: https://orcid.org/0000-0001-7457-7716)
- Witold Kosmala (ORCID: https://orcid.org/0000-0002-2101-9224)
Institutions
- Central European Institute of Technology (CZ)
- Serbian Academy of Sciences and Arts (RS)
- University of Kragujevac (RS)
- China Medical University (TW)
- University of Belgrade (RS)
- Central European Institute of Technology (AT)
- China Medical University Hospital (TW)
- Appalachian State University (US)
- Mathematical Institute of the Serbian Academy of Sciences and Arts
- Brno University of Technology (CZ)
Publication Details
- Journal
- Journal of Inequalities and Applications
- Published
- 2025-10-15
- DOI
- https://doi.org/10.1186/s13660-025-03375-7
- Primary Topic
- Mathematical Inequalities and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Grantová Agentura České Republiky
- Science Fund of the Republic of Serbia