ON THE CESARO SUMMABILITY OF ULTRASPHERICAL SERIES

On the Restricted Cesaro Summability of Double Fourier Series

and po.biu, v), («, v), has been considered by a number of writers. Gergen and Littauer [4, Theorems IV and V] have treated the problem of the boundedness, and convergence in the Pringsheim sense, of ...

On the Mean Summability by Cesaro Method of Fourier Trigonometric Series in Two-weighted Setting

It is well known that (see [9]) Cesaro means of 2π-periodic functions f ∈ Lp(T) (1 ≤ p ≤ ∞) converges by norms. Hereby T is denoted the interval (−π,π). The problem of the mean summability in weighted Lebesgue spaces has been investigated in [6]. A 2π-periodic nonnegative integrable function w : T→R1 is called a weight function. In the sequel by L p w(T), we denote the Banach function space of ...

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 ...

On absolute generalized Norlund summability of double orthogonal series

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

On Summability of Double Series*