On the asymptotic behaviour of \(\varphi\)-means. (English) Zbl 0833.26004
The author offers a generalization of a result by R. P. Boas and J. L. Brenner [J. Math. Anal. Appl. 123, 262-264 (1987; Zbl 0614.26001)], which states that, under certain conditions, the limit of \(f^{-1}(\sum p_k f(x_k + t)) - t\) as \(t\) goes to \(+ \infty\) is \(\sum p_k x_k\) \((\sum p_k = 1)\), to (Stieltjes) integral means on masses with compact support.
Reviewer: J.Aczél (Waterloo/Ontario)
MSC:
26A12 | Rate of growth of functions, orders of infinity, slowly varying functions |
26A06 | One-variable calculus |
26A15 | Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable |
26A48 | Monotonic functions, generalizations |
28A25 | Integration with respect to measures and other set functions |