Theorems concerning the summability of series by boreľs exponential method

Tauberian Theorems by Weighted Summability Method

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...

One-sided Tauberian Theorems for Dirichlet Series Methods of Summability

We extend recently established two-sided or O-Tauberian results concerning the summability method Dλ,a based on the Dirichlet series ∑ ane−λnx to one-sided Tauberian results. More precisely, we formulate one-sided Tauberian conditions, under which Dλ,a-summability implies convergence. Our theorems contain various known results on power series methods of summability and, in the so-called high in...

Limit summability of ultra exponential functions

In [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.Also, we exhibited the topic of limit summability of real functions in [2,3]. Inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. Finally, we pose an unsolved problem aboutthem.

Summability Method of Conjugate Series of Its Fourier Series (communicated by Hüseyin Bor)

Recently, Lal [9] has determined the degree of approximation of function belonging to Lip α and weighted classes using Product C . Np summability with non-increasing weights{pn}. In this paper, we determine the degree of approximation of function f̃ , conjugate to a 2π-periodic function f belonging to Lip (ξ (t), r)−class using semi-monotonicity on the generating sequence {pn} with proper set of...