In this paper we have characterized the space of summa-bility kernels for the case p = 1 and p = 2. For other values of p we give a necessary condition for a function Λ to be a summability kernel. For the case p = 1, we have studied the properties of measures which are transferred from M (Z) to M (R) by summability kernels. Further, we have extended every l p sequence to L q (R) multipliers for...

In this paper, we retrieve slow oscillation of a real sequence u = (u n) out of (C, 1) summability of the generator sequence (V (0) n (Δu)) of (u n) under some additional condition. Consequently, we recover convergence or subsequential convergence of (u n) out of (C, 1) summability of (u n) under certain additional conditions that control oscillatory behavior of the sequence (u n).

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.

We show that a real bounded sequence (xn) is Cesaro convergent to l if and only the of averages with indices in [αk,αk+1) converges for all α>1 . If, addition, (xn)...

In this paper, we obtain fuzzy approximations to fuzzy differentiable functions by means of fuzzy linear operators whose positivity condition and classical limits fail. In order to get more powerful results than the classical approach we investigate the effects of matrix summability methods on the fuzzy approximation. So, we mainly use the notion of A-statistical convergence from summability th...

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...

We study Tauberian conditions for the existence of Cesàro limits in terms of the Laplace transform. We also analyze Tauberian theorems for the existence of distributional point values in terms of analytic representations. The development of these theorems is parallel to Tauber’s second theorem on the converse of Abel’s theorem. For Schwartz distributions, we obtain extensions of many classical ...

In this paper, the long-time behavior of Cesaro mean fundamental solution for fractional Heat equation corresponding to random time changes in Brownian motion is studied. We consider both stable subordinators leading equations with Caputo-Djrbashian derivative and more general cases differential-convolution operators, particular, distributed order derivatives.

Abstract. In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the LaplaceBeltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general properties and representation by the eigenfunctions of the Laplace-Beltrami operator of the Liouville space L 1 is used. For the orders of Riesz means...