One-sided Tauberian conditions for (C, 1) summability method of integrals

WOS: 000299541100014Let f be a real valued function which is continuous on [0, infinity). In this paper we prove a Tauberian-like theorem to retrieve slow oscillation of s(x) = integral(x)(0) f (t) dt out of its (C, 1) summability of the generator function nu(1)(x) and some additional conditions. As a corollary we recover convergence of s(x). (C) 2011 Elsevier Ltd. All rights reserved