Abstract
We prove that the strongest (largest convex) solution of the functional inequality
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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References
Alsina, C.,On countable products and algebraic convexifications of probabilistic metric spaces. Pacific J. Math.76 (1978), 291–300.
Alsina, C.,On a family of functional inequalities. InGeneral Inequalities 2, Birkhäuser, Basel 1981, pp. 419–427.
Schweizer, B. andSklar, A.,Probabilistic metric spaces. Elsevier, North Holland-New York, 1983.
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Alsina, C. On convex triangle functions. Aeq. Math. 26, 191–196 (1983). https://doi.org/10.1007/BF02189682
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DOI: https://doi.org/10.1007/BF02189682