For a non-decreasing sequence of positive integers tending to infinity $\lambda=(\lambda_m)$ such that $\lambda_{m+1}-\lambda_m\leq 1$, $\lambda_1=1$; $(V,\lambda)$-summability has been defined as the limit generalized de la Val\'{e}e-Pousin sequence, [10]. In present research, we will establish some Tauberian, Abelian and Core Theorems related $(V,\lambda)$-summability.

Abstract In this paper, we construct the complex Shepard operators to approximate continuous and complex-valued functions on unit square. We also examine effects of regular summability methods approximation by these operators. Some applications verifying our results are provided. To illustrate theorems graphically consider real or imaginary part function being approximated use contour lines mod...

in this paper, we define and study the notion of the real-valued functions on a frame $l$. we show that $f(l) $, consisting of all frame homomorphisms from the power set of $mathbb{r}$ to a frame $ l$, is an $f$-ring, as a generalization of all functions from a set $x$ into $mathbb r$. also, we show that $f(l) $ is isomorphic to a sub-$f$-ring of $mathcal{r}(l)$, the ring of real-valued continu...

In this paper, we obtain one-sided and two-sided Tauberian conditions of Landau Hardy types for (C,1,0) (C,0,1) summability methods improper double integrals under which convergence follows from integrals. We give similar results (C,1,1) method general, in terms the concepts slowly decreasing (resp. oscillating) strong functions different senses Ces?ro real or complex-valued locally integrable ...

We consider the linear elliptic equation −div(a∇u) = f on some bounded domain D, where a has the form a = exp(b) with b a random function defined as b(y) = ∑ j≥1 yjψj where y = (yj) ∈ RN are i.i.d. standard scalar Gaussian variables and (ψj)j≥1 is a given sequence of functions in L∞(D). We study the summability properties of Hermite-type expansions of the solution map y 7→ u(y) ∈ V := H 0 (D), ...

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...