Alsina, Claudi On convex triangle functions. (English) Zbl 0564.39006 Aequationes Math. 26, 191-196 (1983). The author considers the class \(\Delta^+\) of probability distribution functions on the real line, which are left continuous and vanish at the origin. If \(\epsilon_ a\in \Delta^+\) has the single point a of discontinuity, \(a\geq 0\), and if the function \(\tau: \Delta^+\times \Delta^+\to \Delta^+\) has the properties \((i)\quad \tau (F,\epsilon_ 0)=F,\) (ii) \(\tau\) (F,G)\(\leq \tau (H,K)\), if \(F\leq H\), \(G\leq K\), (iii) \(\tau (F,G)=\tau (G,F)\), \((iv)\quad \tau (\tau (F,G),H)=\tau (F,\tau (G,H)),\) \(F,G,H,K\in \Delta^+\), then the largest solution of the inequality \(\tau ((F+G)/2,(H+K)/2)\leq (\tau (F,H)+\tau (G,K))/2\) is \(\max (F+G-1,0)\). Reviewer: A.B.Buche Cited in 1 Document MSC: 39B72 Systems of functional equations and inequalities 60E05 Probability distributions: general theory Keywords:triangle function; convex; functional inequality; distribution functions; largest solution PDFBibTeX XMLCite \textit{C. Alsina}, Aequationes Math. 26, 191--196 (1983; Zbl 0564.39006) Full Text: DOI EuDML References: [1] Alsina, C.,On countable products and algebraic convexifications of probabilistic metric spaces. Pacific J. Math.76 (1978), 291–300. · Zbl 0412.54007 [2] Alsina, C.,On a family of functional inequalities. InGeneral Inequalities 2, Birkhäuser, Basel 1981, pp. 419–427. [3] Schweizer, B. andSklar, A.,Probabilistic metric spaces. Elsevier, North Holland-New York, 1983. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.