Necessary and sufficient conditions for the Schur harmonic convexity or concavity of the extended mean values

• Wei-Feng Xia ^[1] ; Yu-Ming Chu ^[1] ; Gen-Di Wang ^[1]
  1. [1] Huzhou Teachers College
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 52, Nº. 1, 2011, págs. 121-132
• Idioma: inglés
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• Resumen

  • In this paper, we prove that the extended values E(r, s; x, y) are Schur harmonic convex (or concave, respectively) with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (r, s) ∈ {(r, s) : s ≥ −1, s ≥ r, s + r + 3 ≥ 0} ∪ {(r, s) : r ≥ −1, r ≥ s, s+r + 3 ≥ 0} (or {(r, s) : s ≤ −1, r ≤ −1, s+r + 3 ≤ 0}, respectively).