| Abstract: | It is known that the Power Means tend to the maximum of their arguments when the exponents tend to ({+infty}). We give certain necessary and sufficient conditions for a 1-parameter family of quasi-arithmetic means generated by functions satisfying certain smoothness conditions to have an analogous property. Our results are deeply connected with operators introduced by Mikusiński and Páles in the late 1940s and late 1980s, respectively. The main result is a generalization of the author’s earlier results. |
