The concept of moment differentiation is extended to the class summable functions, giving rise differential properties. main result leans on accurate upper estimates for integral representation derivatives functions under exponential-like growth at infinity, and appropriate deformation integration paths. theory applied obtain summability results certain family generalized linear partial equatio...

We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated, first, in terms of single sums and, finally, in terms of values of special functions.

In this article we introduce the notion of different types of statistically convergent and statistically null fuzzy real-valued double sequence spaces. We study their different properties like solidness, symmetric, convergence free, sequence algebra etc. The fuzzy real-valued Cesàro summable double sequence space is introduced. A relation between strongly p-Cesàro summability and bounded statis...

Abstract The main object of this article is to introduce the concepts ( f, ρ )− statistical convergence order α and strong summability sequences real numbers give some inclusion relations between these spaces.

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 ...

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...

After a brief summary of Tauberian conditions for ordinary sequences of numbers, we consider summability of double sequences of real or complex numbers by weighted meanmethods which are not necessarily products of related weighted mean methods in one variable. Our goal is to obtain Tauberian conditions under which convergence of a double sequence follows from its summability, where convergence ...