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f(x)/y^2 - f(y)/x^2 <= (1/x - 1/y)^2

Source: JOM 2024 P3

February 29, 2024
algebrafunctional equation

Problem Statement

Find all functions f:R+→R+f:\mathbb{R}^+\rightarrow\mathbb{R}^+ such that for all x,y∈R+x, y\in\mathbb{R}^+, f(x)y2−f(y)x2≤(1x−1y)2 \frac{f(x)}{y^2} - \frac{f(y)}{x^2} \le \left(\frac{1}{x}-\frac{1}{y}\right)^2 (R+\mathbb{R}^+ denotes the set of positive real numbers.)
(Proposed by Ivan Chan Guan Yu)
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