Ideal convergence generated by double summability methods

Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's sense

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 ...

Abel summability and angular convergence

We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.

On Ideal Version of Lacunary Statistical Convergence of Double Sequences

For any double lacunary sequence θrs = {(kr, ls)} and an admissible ideal I2 ⊆ P(N×N), the aim of present work is to define the concepts of Nθrs(I2)− and Sθrs(I2)−convergence for double sequence of numbers. We also present some inclusion relations between these notions and prove that Sθrs(I2)∩`∞ and S2(I2)∩ `∞ are closed subsets of `∞, the space of all bounded double sequences of numbers.

On Ideal Convergence of Double Sequences in Probabilistic Normed Spaces

One of the generalizations of statistical convergence is I-convergence which was introduced by Kostyrko et al. [12]. In this paper, we define and study the concept of I-convergence, I∗-convergence, I-limit points and I-cluster points of double sequences in probabilistic normed space. We discuss the relationship between I2-convergence and I ∗ 2 -convergence, i.e., we show that I ∗ 2 -convergence...

On Summability of Double Series*