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J Ascel (1965, p241,246,196 ,281,286): in his' lectures on Functional equations and their applications)' pictures attached on page (196) Azcel, Describes a condition for a real valued function as intern: if\forall x>y,in A,B F(x,y)\s in x,y and F(x,y) is in (y,x) for all ywhere F(x,y) is presumably some kind of mean, or mediality relation,s the domain of the function. Does this have an analogue for functions of single variable?or otherwise just a many valued monotonic kind of someone know what this means, in the context of single variable “Dear William,F is a function of two variables, which are extremities of an interval. Without obstacles we can reformulate:F* is a function that associates a real number to a compact interval, F*( x,y ) = F(x,y). Internality of F on a,b can be perceived as follows: the value associated by F* to any closed subinterval x,y of a,b lies in (x,y). In French, a similar (somewhat weaker) property is:Soit g une fonction d finie sur un intervalle I. On dit que I est stable par g si et seulement si g(I) est un sous-ensemble de I.