The base family for a continuous mean and the representation of quasi-arithmetic means. (Spanish. English summary) Zbl 1370.26060
Summary: As development of the theory of dyadic iterations of a function, we present the concept of base family for continuous and symmetric means. Besides allowing a satisfactory answer to the question of lack of essential uniqueness in quasi-arithmetic representation of the mean, the concept of based family provides an appropriate tool to use the theory of iteration for the construction of continuous solutions for the self-conjugate functional equation.