Publication result detail

Monotonicity character of convex combinations of two sequences generated by the square of the cube root function

STEVIC, S.; IRIČANIN, B.; KOSMALA, W.; ŠMARDA, Z.

Original Title

Monotonicity character of convex combinations of two sequences generated by the square of the cube root function

English Title

Monotonicity character of convex combinations of two sequences generated by the square of the cube root function

Type

WoS Article

Original 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.

English 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.

Keywords

Real sequence;Monotone sequence;Eventual monotonicity;The cube root function

Key words in English

Real sequence;Monotone sequence;Eventual monotonicity;The cube root function

Authors

STEVIC, S.; IRIČANIN, B.; KOSMALA, W.; ŠMARDA, Z.

Released

15.10.2025

Periodical

Journal of Inequalities and Applications

Volume

2025

Number

122

State

Swiss Confederation

Pages count

12

URL

https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-025-03375-7

BibTex

@article{BUT199211,
  author="{} and  {} and  {} and Zdeněk {Šmarda}",
  title="Monotonicity character of convex combinations of two sequences generated by the square of the cube root function",
  journal="Journal of Inequalities and Applications",
  year="2025",
  volume="2025",
  number="122",
  pages="12",
  doi="10.1186/s13660-025-03375-7",
  url="https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-025-03375-7"
}