## On the simultaneous associativity of F(x,y) and x+y-F(x,y).(English)Zbl 0444.39003

### MSC:

 39B99 Functional equations and inequalities
Full Text:

### References:

 [1] Aczél, J.,Lectures on functional equations and their applications. Academic Press, New York, 1966. · Zbl 0139.09301 [2] Frank, M. J.,Associativity in a class of operations on spaces of distribution functions. Aequationes Math.12 (1975), 121–144. · Zbl 0308.39009 [3] Kimberling, C.,On a class of associative functions. Publ. Math. Debrecen20 (1973), 21–39. · Zbl 0276.26011 [4] Ling, C.-H.,Representation of associative functions. Publ. Math. Debrecen12 (1965), 189–212. · Zbl 0137.26401 [5] Mostert, P. S. andShields, A. L.,On the structure of semi-groups on a compact manifold with boundary. Ann. Math.65 (1957), 117–143. · Zbl 0096.01203 [6] Moynhan, R.,On the class of {$$\tau$$} T semigroups of probability distribution functions II. Aequationes Math.17 (1978), 19–40. · Zbl 0386.22005 [7] Paalman-de Miranda, A. B.,Topological semigroups. InMathematical centre tracts, No. 11, Mathematisch Centrum Amsterdam, 1964. · Zbl 0136.26904 [8] Schweizer, B. andSklar, A.,Associative functions and statistical triangle inequalities. Publ. Math. Debrecen8 (1961), 169–186. · Zbl 0107.12203 [9] Schweizer, B. andSklar, A.,Associative functions and abstract semigroups. Publ. Math. Debrecen10 (1963), 69–81. [10] Schweizer, B. andSklar, A.,Operations on distribution functions not derivable from operations on random variables, Studia Math.52 (1974), 43–52. · Zbl 0292.60035 [11] Sklar, A.,Problem (P126). Aequationes Math.11 (1974), 312–313.
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