{
  "problem_id": "IMO2026-P5",
  "day": 2,
  "number": 5,
  "language": "en",
  "statement_markdown": "Let $\\mathbb{R}_{>0}$ be the set of positive real numbers. Determine all functions $f\\colon \\mathbb{R}_{>0}\\to\\mathbb{R}_{>0}$ such that\n$$\\sqrt{\\frac{x^2+f(y)^2}{2}} \\;\\ge\\; \\frac{f(x)+y}{2} \\;\\ge\\; \\sqrt{x\\,f(y)}$$\nfor every $x,y\\in\\mathbb{R}_{>0}$.",
  "normalization_changes": [
    "Rendering-only: MathJax SVG glyphs transcribed to LaTeX ($...$ / $$...$$). No semantic change.",
    "Whitespace collapsed; problem parts kept as in source (e.g. (a)/(b), bulleted steps)."
  ],
  "semantic_content_unchanged": true
}