Beta-type means

Abstract

Based on the relationship between the Beta and the Euler Gamma function, beta-type functions of several variables, generated by a single variable function, are introduced. Applying the method of iterative functional equations, all means of beta-type are determined and some of their properties are discussed.     

The logarithmic Cauchy quotient mean

Motivated by recent results on beta-type functions, a new family of means, which are of logarithmic Cauchy quotient type, are determined and characterized.