in [1] we uniquely introduced ultra exponential functions (uxpa) and de nednext step of the serial binary operations: addition, multiplication and power.also, we exhibited the topic of limit summability of real functions in [2,3]. inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. finally, we pose an unsolved problem aboutthem.

In classical complex analysis, the theorems of Weierstrass, Montel and Hurwitz are of great use in very many contexts. The main goal of the present paper is to relax their strong hypotheses via the concept of A-statistical convergence, where A is a nonnegative regular summability matrix. The A-statistical convergence method is defined in the following way. Let A := [ajn] (j, n ∈ N := {1, 2, 3, ...

* Correspondence: [email protected] Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India Full list of author information is available at the end of the article Abstract In this article, we prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical A-summability. We also study the rate of statistical A-summability of p...

and a method A of summability by means of which a given sequence Su S2, • • • is summable to <r as w—»oo. If a sequence sn is summable A, we say that A {sn} exists and that sn belongs to the summability field of A. If sn is summable A to <r, we say that A {sn} = <r. The method A is regular if A {sn} = lim sn whene...

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.

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 ...