A new general Boas-type inequality and related Cauchy-type means

Abstract

We prove a new Boas-type inequality in a context of topological spaces and general $\sigma$-finite Borel measures. This enables us to introduce an one-parameter class of non-negative Boas differences and examine their properties, such as continuity and log-convexity. By proving the related Galvani's theorem and mean-value theorems of the Lagrange and Cauchy type we establish a new class of two-parameter Cauchy-type means.