Limit properties in a family of quasi-arithmetic means

Abstract

It is known that the family of power means tends to maximum pointwise if we pass argument to infinity. We will give some necessary and sufficient condition for the family of quasi-arithmetic means generated by a functions satisfying certain smoothness conditions to have analogous property.

10 pages

Cited by in corpus (5)

• On Kedlaya type inequalities for weighted means
• Invariance property for extended means
• Quasiarithmetic-type invariant means on probability space
• Interval-type theorems concerning quasi-arithmetic means
• On the $L^1$ and pointwise divergence of continuous functions