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...

Quite recently, Bor (2021) [22] has proved two main theorems dealing with absolute Riesz summability factors of infinite series and Fourier by using an almost increasing sequence. In this paper, we have generalized these to the | A , p n k method.

Abstract The order of integration is valid to characterize linear processes; but it is not appropriate for non-linear worlds. We propose the concept of summability (a re-scaled partial sum of the process being Op(1)) to handle non-linearities. The paper shows that this new concept, S (δ): (i) generalizes I (δ); (ii) measures the degree of persistence as well as of the evolution of the variance;...

We prove a general theorem on |N̄,pn;δ|k summability factors, which generalizes a theorem of Bor (1994) on |N̄,pn|k summability factors, under weaker conditions by using an almost increasing sequence. 2000 Mathematics Subject Classification. Primary 40D15, 40F05, 40G99.

in this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$i$-statistical convergence and‎ ‎$i$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{n}$) and‎ ‎introduce the notions of $i$-statis...