Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417731 | Journal of Mathematical Analysis and Applications | 2015 | 7 Pages |
Abstract
Let h:[1,â)â[0,â) be a function with the properties that there exists x0â¥1 such that hâC1([x0,â)), h(x0)>0, hâ²(x)>0 for all xâ¥x0 and limxâââ¡h(x)=â. We prove that if a:Nâ[0,â) and kâ¥1 then, ânâ¤xa(n)â½[h(x)]k if and only if for every function f:[0,1]âR such that xkâ1f(x) is Riemann integrable the following equality holdslimxâââ¡1[h(x)]kâx0
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Dumitru Popa,