Overconvergence and $(C,\,1)$ summability

Wavelet Approximations using (Λ⋅C1) Matrix-Cesaro Summability Method of Jacobi Series

In this paper, an application to the approximation by wavelets has been obtained by using matrix-Cesaro (Λ⋅C1) method of Jacobi polynomials. The rapid rate of convergence of matrix-Cesaro method of Jacobi polynomials are estimated. The result of Theorem (6.1) of this research paper is applicable for avoiding the Gibbs phenomenon in intermediate levels of wavelet approximations. There are major ...

Abel summability and angular convergence

We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.

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...

Geometric Overconvergence of Rational Functions in Unbounded Domains

(iv) the sequence {rn(z)}Z=ι converges geometrically to an analytic extension of / on some open set in the plane containing E. The aim of the present paper is to investigate the phenomenon of overconvergence in the case where E is a closed line segment [α, b] and the hypothesis (iii) above is weakened to allow accumulation points of poles at the endpoints of £", i.e., assumption (iii) is replac...