Journal ArticleDOI
Statistical convergence of multiple sequences
Reads0
Chats0
TLDR
In this article, the authors extend the concept of convergence from single sequences to multiple sequences of real or complex numbers and obtain the following result: the Fourier series of f is statistically convergent to $f ({\bf t})$ uniformly on the d-dimensional torus.Abstract:
We extend the concept of and basic results on statistical convergence from
ordinary (single) sequences to multiple sequences of (real or complex) numbers.
As an application to Fourier analysis, we obtain the following Theorem 3: (i)
If $f \in L(\textrm{log}^{+} L)^{d-1}(\mathbb{T}^d)$, where $\mathbb{T}^d := [-\pi, \pi)^{d}$
is the d-dimensional torus, then the Fourier
series of f is statistically convergent to $f({\bf t})$
at almost every ${\bf t} \in \mathbb{T}^d$; (ii) If $f \in C(\mathbb{T}^d)$, then the
Fourier series of f
is statistically convergent to $f ({\bf t})$ uniformly on $\mathbb{T}^d$.read more
Citations
More filters
Book ChapterDOI
Statistical Convergence of Double Sequences
Mursaleen,Osama H. H. Edely +1 more
TL;DR: In this article, the authors define and study statistical analogue of convergence and Cauchy for double sequences and establish the relation between statistical convergence and strongly Cesaro summable double sequences.
Journal ArticleDOI
λ-Statistical convergence of order α
Rifat Çolak,Çiğdem A. Bektaş +1 more
TL;DR: In this paper, the concept of λ-statistical convergence of order α was introduced, and some relations between the λ statistical convergence and strong (V, λ)-summability were given.
Journal ArticleDOI
I and I*-convergence of double sequences
TL;DR: In this article, the notions of I and I*-convergence of double sequences in real line as well as in general metric spaces were studied and the interrelationship between these two types of convergence was investigated.
Journal ArticleDOI
On ℑ-Cauchy sequences
TL;DR: In this article, the authors studied the space where the convergence and Cauchy sequences in metric spaces are ideal. But they did not define the conditions in which a set of singletons is an ideal.
Journal Article
On I and I ∗ −convergence of double sequences
TL;DR: In this paper, the authors introduced the con- cept of I ∗ -convergence for double sequences and proved some results for I and I ∆ -consvergence of double sequences.
References
More filters
Book
An Introduction to the Theory of Numbers
TL;DR: The fifth edition of the introduction to the theory of numbers has been published by as discussed by the authors, and the main changes are in the notes at the end of each chapter, where the author seeks to provide up-to-date references for the reader who wishes to pursue a particular topic further and to present a reasonably accurate account of the present state of knowledge.
Journal ArticleDOI
On statistical convergence
TL;DR: In this article, it is shown that Statistical convergence cannot be included by any matrix metbod. And two Tauberian theorems are proved: one uses the Tauberians condition Axi, = 0(1/Ar), which is shown to be ''best possible,\" and the other is concerned with gap sequences.
Journal ArticleDOI
The Integrability of Certain Functions and Related Summability Methods
TL;DR: The Integrability of Certain Functions and Related Summability Methods as discussed by the authors is a seminal work in the field of algebraic geometry, and it has been used extensively in many applications.