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...

In this paper, we introduce the concept of λ-statistical convergence in n-normed spaces. Some inclusion relations between the sets of statistically convergent and λ-statistically convergent sequences are established. We find its relations to statistical convergence, (C,1)-summability and strong (V, λ)-summability in n-normed spaces.

Purpose: The purpose of the present paper is to study the product (N, pn) (C, 1) summability of a sequence of Fourier coefficients which extends a theorem of Prasad. Methods: We use Np. C 1 summability methods with dropping monotonicity on the generating sequence {pn − k} (that is, by weakening the conditions on the filter, we improve the quality of digital filter). Results: Let Bn(x) denote th...

In this paper,  we determine necessary and sufficient Tauberian conditions under which convergence in Pringsheim's sense of a double sequence of fuzzy numbers follows from its $(C,1,1)$ summability. These conditions are satisfied if the double sequence of fuzzy numbers is slowly oscillating in different senses. We also construct some interesting double sequences of fuzzy numbers.

We consider the summability of oneand multi-dimensional trigonometric Fourier series. The Fejér and Riesz summability methods are investigated in detail. Different types of summation and convergence are considered. We will prove that the maximal operator of the summability means is bounded from the Hardy space Hp to Lp, for all p > p0, where p0 depends on the summability method and the dimensio...

In the present innovative pursuit, the generalized Nörlund summability method, that is, the (N, c, d) summation process of Fourier series of f (x) as well defined by Borwein [4] has been invoked to approximate the function f (x) belonging to Lip M α (0 < α < 1 ) and M being some constant. Here it is worth-emphasising that not only mere approximation, but also the constants appeared in the proce...

Let $(u_n)$ be a sequence of fuzzy numbers.  We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces`{a}ro summability method are established as particular cases.

This paper generalises a well-known theorem on ${\mid{C},\rho\mid}_\kappa$ summability to the $\varphi-{\mid{C},\rho;\beta\mid}_\kappa$ of an infinite series using almost increasing and $\delta$-quasi monotone sequence.

In this paper we shall discuss the relation of the convergence or (C, 1) summability of a sequence to that of its subsequences. Some analogous questions for subseries have been considered [ö]. Let {sn} be an arbitrary sequence. We can obtain a 1-1 map of its infinite subsequences on the interval 0 < / ^ l as follows. Let /= .a ia 2 a 3 • • • be the infinite dyadic expansion of a point / of the ...