Year: 2026
Type: article
Abstract: In 2016, Dannan and Sitnik established the notable Damascus inequality, which features a symmetric structure under a multiplicative constraint. In this study, we consider the natural generalisation of this inequality by characterising all positive integers m and n such that the inequality $$\begin{aligned} \sum _{j=1}^m\frac{x_j^n-1}{x_{j}^{n+1}+1}\leqslant 0 \end{aligned}$$ ∑ j = 1 m x j n - 1 x j n + 1 + 1 ⩽ 0 holds for any positive real numbers $$x_1, \ldots , x_m$$ x 1 , … , x m with $$\prod _{j=1}^mx_j=1$$ ∏ j = 1 m x j = 1 . Our approach relies on the theories of GA-convexity and Sturm’s sequence. For the cases where the inequality fails, we also investigate the topological properties of the set of non-solutions.
Source: The Ramanujan Journal
Institutions: University of Hong Kong, Université de Caen Normandie
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W7130853480