Properties of a class of mean dependent on a parameter

Abstract

Abstract Some properties of a new class of binary symmetric mean Mp(a,b) $M_{p} (a,b)$ which depends on two positive numbers a and b, as well as a positive parameter p, are investigated. The logarithmic mean and arithmetic mean are two members of this class. It is shown that, for all values of the parameter p, the set of p-dependent means Mp(a,b) $M_{p} (a,b)$ is bounded above by the mean M∞(a,b) $M_{\infty } (a,b)$.

Keywords

• Means
• Series
• Convergence
• Arithmetic
• Bounded