An Elementary Tauberian Theorem of Nonlinear Type

Abstract

We find a nonlinear condition on $f \in {C^2}(0,\infty )$ which, when coupled with the assumption $\lim \inf |f(t)|/t < \infty$, implies $f \sim At$ and $f’ \to A$. $A$ is some constant and $t \to \infty$ or $t \to 0 +$.

Locations

• Proceedings of the American Mathematical Society - View - PDF