On convex triangle functions |
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| Authors: | Claudi Alsina |
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| Affiliation: | 1. Department de Matemàtiques i Estadística, E.T.S. Arquitectura de Barcelona, Universitat Politècnica de Barcelona, Diagonal 649, Barcelona -28-, Spain
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| Abstract: | We prove that the strongest (largest convex) solution of the functional inequality $$tau left( {frac{{F + G}}{2},frac{{H + K}}{2}} right) le frac{{tau (F,H) + tau (G,K)}}{2},$$ whereF, G, H andK are arbitrary distribution functions, is the triangle function τ(F, G)(x) = Max(F(x) +G(x) ? 1, 0). |
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