Let p be a positive weight function on A:=[1,∞) which is integrable in Lebesgue's sense over
every finite interval (1, x) for 1< x<∞, in symbol: p∈ L loc 1 (A) such that P (x)=∫ 1 xp (t) dt≠ …

In this paper we prove a Tauberian-like theorem to retrieve the slow oscillation of a real-
valued function s (x) from its (C, 1) summability of the generator sequence v (x) and one …

We investigate some Tauberian conditions in terms of the general control modulo of the
oscillatory behavior of integer order of continuous real functions on [0,∞) for (C, 1) …

Let f be a real-valued function which is continuous on [1,∞) and s (x)=∫ 1 xf (t) dt. If the
integral∫ 1∞ f (t) dt= s exists, then limit lim x→∞ 1 log x∫ 1 xs (t) tdt= s (∗) also exists …

Let f be a real valued function which is continuous on [0,∞). In this paper we prove a
Tauberian-like theorem to retrieve slow oscillation of s (x)=∫ 0xf (t) dt out of its (C, 1) …

In this paper, we obtain some new Tauberian conditions in terms of the weighted general
control modulo for the weighted mean method of integrals in order that the converse …

Let 0≠, 𝑝 (𝑥) be a nondecreasing real valued differentiable function on [0,∞) such that 𝑝
(0)= 0 and 𝑝 (𝑥)→∞ as 𝑥→∞. Given a real valued function 𝑓 (𝑥) which is continuous on …

A real-valued continuous function f on [1,∞) is said to be summable by the logarithmic
summability method of integrals (shortly, ℓ summable) if lim x→∞ 1 log x∫ 1 xs (t) tdt exists …

Let 𝑝 (𝑥) be a nondecreasing continuous function on [0,∞) such that 𝑝 (0)= 0 and 𝑝 (𝑡)→∞
as 𝑡→∞. For a continuous function 𝑓 (𝑥) on [0,∞), we define s (t)=∫ 0 tf (u) du and σ α …

For a real-valued continuous function f (x) on [0,∞), we define s (x)=∫ 0 xf (u) du and σ α
(x)=∫ 0 x 1-ux α f (u) du for x> 0. We say that∫ 0∞ f (u) du is (C, α) integrable to L for some …