Abstract In the present paper, a theorem on θ −| T; δ | k summability method of an infinite series is proved, and also by using this method, result trigonometric Fourier obtained.

In this paper a general theorem on absolute weighted mean summability factors has been proved under weaker conditions by using an almost increasing and δ-quasi-monotone sequences.

In this paper we prove that if Λ ∈ M p (R N) and has compact support then Λ is a weak summability kernel for 1 < p <

The paper introduces a new concept of strong summability and statistical convergence of sequence of fuzzy numbers. Further, these two concepts are studied and established relations between them.

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...

After a brief summary of Tauberian conditions for ordinary sequences of numbers, we consider summability of double sequences of real or complex numbers by weighted meanmethods which are not necessarily products of related weighted mean methods in one variable. Our goal is to obtain Tauberian conditions under which convergence of a double sequence follows from its summability, where convergence ...

Fourier orthogonal series with respect to the weight function (1 − |x|2)μ−1/2 on the unit ball in Rd are studied. Compact formulae for the sum of the product of orthonormal polynomials in several variables and for the reproducing kernel are derived and used to study the summability of the Fourier orthogonal series. The main result states that the expansion of a continuous function in the Fourie...