Abstract This paper explores the possibility for summing Fourier series nonlinearly via Pythagorean harmonic mean. It reports on new results this summability with introduction of concepts like smoothing operator and semi-harmonic summation. The is demonstrated to be Kalman filtering linear summability, logistic processing linearized summability. An emerging direct inapplicability seismic-like s...

In this paper we present some results on summability of oneand multi-dimensional Walsh-, Walsh-Kaczmarzand Vilenkin-Fourier series and on the dyadic and Vilenkin derivative. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the martingale Hardy space Hp to Lp (p > p0). For p = 1 we obtain a weak type inequ...

A general theorem is proved which deduces from a Tauberian condition Ti for a summability method, Tauberian condition Ti for the summability method. Recent results of MeyerKönig and Tietz and of Stieglitz are special cases.

In the present paper, a general theorem on | N̄ , pn |k summability factors of infinite series has been proved under more weaker conditions. Also we have obtained a new result concerning the | C, 1 |k summability factors.

In this paper, a known theorem dealing with | N̄, pn |k summability factors of trigonometric Fourier series has been generalized to | N̄, pn, θn |k summability. Some new results have also been obtained.

In this paper, a theorem of Bor and Özarslan [3] dealing with | C,α; β |k summability factors has been generalized for | C,α, γ ; β |k summability methods.

In the year 1921, Nevanlinna [7] suggested and discussed an interesting method of summation called Nq-method. Moursund [5] applied this method for summation of Fourier series and its conjugate series. Later, Moursund [6] developed Nqp-method (where p is a positive integer) and applied it to pth derived Fourier series. Samal [9] discussed Nqαmethod (0 ≤ α < 1) and studied absolute Nqα-summabilit...

Abstract: Degree of approximation of functions of different classes has been studied by several researchers by different summability methods. In the proposed paper, we have established a new theorem for the approximation of a signal (function) belonging to the W(L r , (t))-class by (N, p n , q n )(E, s)-product summability means of a Fourier series. The result obtained here, generalizes several...

A simple structure of the multiple Laguerre polynomial expansions is used to study the Cess aro summability above the critical index for the convolution type Laguerre expansions. The multiple Laguerre polynomial expansion of an`1-radial function f 0 (jxj) is shown to be an`1-radial function that coincides with the Laguerre polynomial expansion of f 0 , which allows us to settle the problem of s...

In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence, we prove a Korovkin type approximation theorem for sequences of positive linear operator defined on C∗(R) which is the space of all 2π-periodic and continuous functions on R, the set of all real numbers. We also compute the rates of statistical A-summability of sequence of positiv...