scholarly journals On the Statistical Convergence of Order α in Paranormed Space

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 483 ◽  
Author(s):  
Sinan ERCAN
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Topological Properties ◽  
Cesàro Summability ◽  
Paranormed Space ◽  
Cesaro Summability ◽  
New Concepts ◽  
Inclusion Relations

The aim of the present work is to introduce notions of statistical convergence, strongly p-Cesàro summability and the statistically Cauchy sequence of order α in paranormed spaces. Some certain topological properties of these new concepts are examined. Furthermore, we introduce the some inclusion relations among them.

Deferred Cesàro summability and statistical convergence for double sequences of sets

2021 ◽  
pp. 1-9
Author(s):  
Uğur Ulusu ◽  
Esra Gülle
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesàro Mean ◽  
Cesaro Summability ◽  
Cesaro Mean

The main purpose of this paper is introduced the concept of deferred Cesàro mean in the Wijsman sense for double sequences of sets and then presented the concepts of strongly deferred Cesàro summability and deferred statistical convergence in the Wijsman sense for double sequences of sets. Also, investigate the relationships between these concepts and then to prove some theorems associated with the concepts of deferred statistical convergence in the Wijsman sense for double sequences of sets is purposed.

scholarly journals Ideally Statistical Convergence in n-normed Space

2020 ◽  
pp. 75-84
Author(s):  
Nazneen Khan ◽  
Amani Shatarah
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Topological Properties ◽  
Normed Spaces

The aim of the article is to extend the concept of Ideally statistical convergence from 2 normed spaces to n-normed space. We have also study and prove some important algebraic and topological properties of Ideally-statistical convergence of real sequences in n-normed space. In the last part of this article we obtain a criterion for I-statistically Cauchy sequence in n-normed space to be I-statistically Cauchy with respect to ∥.∥∞.

scholarly journals Cesàro summability and Lebesgue points of higher dimensional Fourier series

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Lebesgue Point ◽  
Maximal Functions ◽  
Cesàro Means ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Lebesgue Points ◽  
New Concepts ◽  
Higher Dimensional ◽  
Different Types

<p style='text-indent:20px;'>We give four generalizations of the classical Lebesgue's theorem to multi-dimensional functions and Fourier series. We introduce four new concepts of Lebesgue points, the corresponding Hardy-Littlewood type maximal functions and show that almost every point is a Lebesgue point. For four different types of summability and convergences investigated in the literature, we prove that the Cesàro means <inline-formula><tex-math id="M1">\begin{document}$ \sigma_n^{\alpha}f $\end{document}</tex-math></inline-formula> of the Fourier series of a multi-dimensional function converge to <inline-formula><tex-math id="M2">\begin{document}$ f $\end{document}</tex-math></inline-formula> at each Lebesgue point as <inline-formula><tex-math id="M3">\begin{document}$ n\to \infty $\end{document}</tex-math></inline-formula>.</p>

Applications of Statistical Convergence of order (η, δ + γ) in difference sequence spaces of fuzzy numbers

2020 ◽  
pp. 1-9
Author(s):  
Swati Jasrotia ◽  
Uday Pratap Singh ◽  
Kuldip Raj
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Cesàro Summability ◽  
Matlab Software ◽  
Cesaro Summability ◽  
Set Up ◽  
Difference Sequence Spaces

In this article, we introduce and study some difference sequence spaces of fuzzy numbers by making use of λ-statistical convergence of order (η, δ + γ) . With the aid of MATLAB software, it appears that the statistical convergence of order (η, δ + γ) is well defined every time when (δ + γ) > η and this convergence fails when (δ + γ) < η. Moreover, we try to set up relations between (Δv, λ)-statistical convergence of order (η, δ + γ) and strongly (Δv, p, λ)-Cesàro summability of order (η, δ + γ) and give some compelling instances to show that the converse of these relations is not valid. In addition to the above results, we also graphically exhibits that if a sequence of fuzzy numbers is bounded and statistically convergent of order (η, δ + γ) in (Δv, λ), then it need not be strongly (Δv, p, λ)-Cesàro summable of order (η, δ + γ).

scholarly journals Statistical Tauberian theorems for Cesàro integrability mean based on post-quantum calculus

2020 ◽  
Vol 9 (3) ◽  
pp. 653-663
Author(s):  
P. Parida ◽  
S. K. Paikray ◽  
B. B. Jena
Keyword(s):  
Continuous Function ◽  
Statistical Convergence ◽  
Tauberian Theorems ◽  
Cesàro Summability ◽  
Quantum Calculus ◽  
Cesaro Summability ◽  
Single Integral ◽  
De La Vallée Poussin

Abstract The notion of statistical convergence is more general than the classical convergence. Tauberian theorems via different ordinary summability means have been established by many researchers. In the present work, we have established some new Tauberian theorems based on post-quantum calculus via statistical Cesàro summability mean of real-valued continuous function of one variable under oscillating behavior and De la vallée Poussin mean of a single integral. Moreover, some remarks and corollaries are provided here to support our theorems.

scholarly journals On(Δm,I)-Statistical Convergence of Orderα

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Mikail Et ◽  
Abdullah Alotaibi ◽  
S. A. Mohiuddine
Keyword(s):  
Statistical Convergence ◽  
Cesàro Summability ◽  
Cesaro Summability

The idea ofI-convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of(Δm,I)-statistical convergence of orderαand strong(Δpm,I)-Cesàro summability of orderαof real sequences and investigated their relationship.

scholarly journals A note on generalized harmonic-Cesàro summability

1984 ◽  
Vol 7 (2) ◽  
pp. 413-414 ◽  
Author(s):  
Hiroshi Hiorkawa
Keyword(s):  
Cesàro Summability ◽  
Cesaro Summability ◽  
Inclusion Relations

This note shows that conjectures proposed byG. Das and P.C. Mohapatra [1] on inclusion relations between two generalized Harmonic-Cesàro methods of summability, are true.

On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence

1989 ◽  
Vol 32 (2) ◽  
pp. 194-198 ◽  
Author(s):  
Jeff Connor
Keyword(s):  
Statistical Convergence ◽  
Summability Method ◽  
Regular Matrix ◽  
Cesàro Summability ◽  
Matrix Summability ◽  
Cesaro Summability ◽  
Definition Of ◽  
Bounded Sequences

AbstractThe definition of strong Cesaro summability with respect to a modulus is extended to a definition of strong A -summability with respect to a modulus when A is a nonnegative regular matrix summability method. It is shown that if a sequence is strongly A-summable with respect to an arbitrary modulus then it is A-statistically convergent and that Astatistical convergence and strong A-summability with respect to a modulus are equivalent on the bounded sequences.

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