(C,α) summability of Walsh–Kaczmarz–Fourier series

Logarithmic Summability of Fourier Series

A set of regular summations logarithmic methods is introduced. This set includes Riesz and Nörlund logarithmic methods as limit cases. The application to logarithmic summability of Fourier series of continuous and integrable functions are given. The kernels of these logarithmic methods for trigonometric system are estimated.

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*

Summability Method of Jacobi Series

In this paper, an application to the approximation by wavelets has been obtained by using matrix-Cesàro (Λ · C1) method of Jacobi polynomials. The rapid rate of convergence of matrix-Cesàro 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 majo...

Product Summability Transform of Conjugate Series of Fourier Series

A known theorem, Nigam 2010 dealing with the degree of approximation of conjugate of a signal belonging to Lipξ t -class by E, 1 C, 1 product summability means of conjugate series of Fourier series has been generalized for the weighted W Lr, ξ t , r ≥ 1 , t > 0 -class, where ξ t is nonnegative and increasing function of t, by ̃ E1 nC n which is in more general form of Theorem 2 of Nigam and Shar...