Strong and absolute almost-convergence of vector functions and related Tauberian theorems ✩

We discuss relations among notions of (C, 1)-convergence, almost-convergence, absolute almostconvergence, and C∗all-convergence of a continuous vector-valued function f (t) as t tends to infinity. Equivalent conditions and Tauberian criterions are obtained, and some examples are exhibited. © 2007 Elsevier Inc. All rights reserved.