Some New Inequalities for the Strictly Monotonic Functions and Positive n-Tuples - Mesihović, Behdžet A. (Sarajevo Journal of Mathematics, 2022)
In this paper we give the generalization of the inequalities \begin{equation*} \begin{split} &n\sum^n_{i=1}a_i^{n} \geq \sum^n_{i=1}a_i^{t} \sum^n_{i=1}a_i^{n-t} \geq \sum^n_{i=1}a_i^{s} \sum^n_{i=1}a_i^{n-s} \geq (\sum^n_{i=1}a_i^\frac{n}{2})^{2} ,\\ & 0 < t < s < \frac{n}{2},\ a_i>0,\forall i \in \{{1,\dots,n}\}, \end{split} \end{equation*} (see [3] and [1, p.~377], and the new results for the strictly monotonic functions and positive n-tuples.