Summability Integrals

On Tauberian Conditions for (c, 1) Summability of Integrals

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) summability of integrals. Moreover, we obtain a Tauberian theorem for a real bounded function on [0,∞).

Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability

In a recent work by the author an extrapolation method, the W-transformation, was developed, by which a large class of oscillatory infinite integrals can be computed very efficiently. The results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper. It is shown in particular that these divergent integrals exist in the sense of Abel summability an...

Summability in topological spaces

On statistical A-summability

Let A = (ank)∞n,k=1 be an infinite matrix and x = (xk) ∞ k=1 a sequence of real or complex numbers. Then the A-transform of x is a sequence Ax = (An(x))where An(x) = ∑ ∞ k=1 ankxk provided that the series converges for each n; and the sequence x is said to be A-summable if Ax is convergent. In this paper we define statistical A-summability of x, that is, x is said to be statistically A-summable...

Absolute matrix summability methods