Gigante, Patrizia On the asymptotic behaviour of \(\varphi\)-means. (English) Zbl 0833.26004 J. Math. Anal. Appl. 192, No. 3, 915-919 (1995). 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) Cited in 1 Document 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 Keywords:integral mean values; monotonic differentiable functions; Stieltjes integral means; masses with compact support Citations:Zbl 0614.26001 PDFBibTeX XMLCite \textit{P. Gigante}, J. Math. Anal. Appl. 192, No. 3, 915--919 (1995; Zbl 0833.26004) Full Text: DOI