Monotonicity character of convex combinations of two sequences generated by the square of the cube root function
Year: 2025
Type: article
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 $[1,+\infty )$ , which is used in the proof of the main result.
Institutions: Serbian Academy of Sciences and Arts, China Medical University, China Medical University Hospital, Mathematical Institute of the Serbian Academy of Sciences and Arts, University of Kragujevac, University of Belgrade, Appalachian State University, Central European Institute of Technology, Brno University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,190
OpenAlex ID: W4415207283