Envelopes of special class of one-parameter families of curves

Abstract

In our recent paper [6] concernig some relations between the logarithmic and arithmetic means we have obtained a family of solutions <f>a of a relevant one-parameter system of functional equations which are of the form 4>a{x) = g{^ ) + $(<*), z>0, where a > 0 is the parameter, and g is a particular solution of the functional equation corresponding to the parameter a = 1. Since g completely describes the one-parameter family of solutions [<$>0)01 > 0 , we call g to be its generator (Fragment tekstu).