Bernstein Operator of Rough λ-statistically and ρ Cauchy Sequences Convergence on Triple Sequence Spaces

2018 ◽  
Vol 85 (1-2) ◽  
pp. 256 ◽  
Author(s):  
S. Velmurugan ◽  
N. Subramanian
Keyword(s):  
Statistical Convergence ◽  
Bernstein Polynomials ◽  
Sequence Spaces ◽  
Bernstein Operator ◽  
Convergence Criteria ◽  
Statistical Limit ◽  
Cauchy Sequences ◽  
Natural Density ◽  
Limit Points

<p>In this article, using the concept of natural density, we introduce the notion of Bernstein polynomials of rough λ−statistically and ρ−Cauchy triple sequence spaces. We define the set of Bernstein polynomials of rough statistical limit points of a triple sequence spaces and obtain to λ−statistical convergence criteria associated with this set. We examine the relation between the set of Bernstein polynomials of rough λ−statistically and ρ− Cauchy triple sequences.</p><p> </p><p> </p>

scholarly journals Wijsman Rough λ Statistical Convergence of Order α of Triple Sequence of Functions

2017 ◽  
Vol 2 (1) ◽  
pp. 07-15
Author(s):  
A. Esi ◽  
N. Subramanian ◽  
M. Aiyub
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Natural Density ◽  
Limit Points ◽  
Cluster Points ◽  
Sequence Of Functions

In this paper, using the concept of natural density, we introduce the notion of Wijsman rough λ statistical convergence of order α triple sequence of functions. We define the set of Wijsman rough λ statistical convergence of order α of limit points of a triple sequence spaces of functions and obtain Wijsman λ statistical convergence of order α criteria associated with this set. Later, we prove that this set is closed and convex and also examine the relations between the set of Wijsman rough λ statistical convergence of order α of cluster points and the set of Wijsman rough λ statistical convergence of order α limit points of a triple sequences of functions.

scholarly journals Statistical limit point theorems

2000 ◽  
Vol 23 (11) ◽  
pp. 741-752 ◽  
Author(s):  
Jeff Zeager
Keyword(s):  
Complex Number ◽  
Limit Point ◽  
Statistical Convergence ◽  
Nonnegative Matrix ◽  
Bounded Sequence ◽  
Regular Matrix ◽  
Number Sequence ◽  
Statistical Limit ◽  
Limit Points

It is known that given a regular matrixAand a bounded sequencexthere is a subsequence (respectively, rearrangement, stretching)yofxsuch that the set of limit points ofAyincludes the set of limit points ofx. Using the notion of a statistical limit point, we establish statistical convergence analogues to these results by proving that every complex number sequencexhas a subsequence (respectively, rearrangement, stretching)ysuch that every limit point ofxis a statistical limit point ofy. We then extend our results to the more generalA-statistical convergence, in whichAis an arbitrary nonnegative matrix.

On rough convergence of ρ-Cauchy sequence of triple sequences

Analysis ◽  
2019 ◽  
Vol 39 (4) ◽  
pp. 129-133
Author(s):  
Ayhan Esi ◽  
M. Aiyub ◽  
N. Subramanian ◽  
Ayten Esi
Keyword(s):  
Cauchy Sequence ◽  
Sequence Spaces ◽  
Cauchy Sequences ◽  
Limit Points ◽  
Cluster Points

Abstract In this paper we define and study rough convergence of triple sequences and the set of rough limit points of a triple sequence. We also investigate the relations between the set of cluster points and the set of rough limit points of Cauchy sequences of triple sequence spaces.

Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space

2020 ◽  
Vol 70 (3) ◽  
pp. 667-680
Author(s):  
Sanjoy Ghosal ◽  
Avishek Ghosh
Keyword(s):  
Metric Space ◽  
Limit Set ◽  
Positive Real ◽  
Weighted Sequence ◽  
Statistical Limit ◽  
Lacunary Statistical Convergence ◽  
Natural Density ◽  
Limit Points ◽  
Cluster Points

AbstractIn 2018, Das et al. [Characterization of rough weighted statistical statistical limit set, Math. Slovaca 68(4) (2018), 881–896] (or, Ghosal et al. [Effects on rough 𝓘-lacunary statistical convergence to induce the weighted sequence, Filomat 32(10) (2018), 3557–3568]) established the result: The diameter of rough weighted statistical limit set (or, rough weighted 𝓘-lacunary limit set) of a sequence x = {xn}n∈ℕ is $\begin{array}{} \frac{2r}{{\liminf\limits_{n\in A}} t_n} \end{array}$ if the weighted sequence {tn}n∈ℕ is statistically bounded (or, self weighted 𝓘-lacunary statistically bounded), where A = {k ∈ ℕ : tk < M} and M is a positive real number such that natural density (or, self weighted 𝓘-lacunary density) of A is 1 respectively. Generally this set has no smaller bound other than $\begin{array}{} \frac{2r}{{\liminf\limits_{n\in A}} t_n} \end{array}$. We concentrate on investigation that whether in a θ-metric space above mentioned result is satisfied for rough weighted 𝓘-limit set or not? Answer is no. In this paper we establish infinite as well as unbounded θ-metric space (which has not been done so far) by utilizing some non-trivial examples. In addition we introduce and investigate some problems concerning the sets of rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space and formalize how these sets could deviate from the existing basic results.

Rough statistical cluster points

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5295-5304
Author(s):  
Salih Aytar
Keyword(s):  
Statistical Convergence ◽  
Cluster Point ◽  
Convergence Criteria ◽  
Finite Dimensional ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Condensation Point ◽  
Statistical Cluster Point ◽  
Dimensional Normed Space ◽  
Cluster Points

In this paper, we define the concepts of rough statistical cluster point and rough statistical limit point of a sequence in a finite dimensional normed space. Then we obtain an ordinary statistical convergence criteria associated with rough statistical cluster point of a sequence. Applying these definitions to the sequences of functions, we come across a new concept called statistical condensation point. Finally, we observe the relations between the sets of statistical condensation points, rough statistical cluster points and rough statistical limit points of a sequence of functions.

scholarly journals Sliding Window Rough measurable function on $I-$ core of triple sequences of Bernstein operator

2019 ◽  
Vol 25 (3) ◽  
pp. 183-193
Author(s):  
Deepmala Rai ◽  
N. Subramanian
Keyword(s):  
Measurable Function ◽  
Bernstein Polynomials ◽  
Sliding Window ◽  
Sequence Spaces ◽  
Bernstein Operator ◽  
Basic Properties

We introduce sliding window rough $I-$ core and study some basic properties of Bernstein polynomials of rough $I-$ convergent of triple sequence spaces and also study the set of all Bernstein polynomials of sliding window of rough $I-$ limits of a triple sequence spaces and relation between analytic ness and Bernstein polynomials of sliding window of rough $I-$ core of a triple sequence spaces.

scholarly journals On I-statistically rough convergence

2019 ◽  
Vol 105 (119) ◽  
pp. 145-150
Author(s):  
Ekrem Savas ◽  
Shyamal Debnath ◽  
Debjani Rakshit
Keyword(s):  
Statistical Convergence ◽  
Statistical Limit ◽  
Limit Points

We introduce rough I-statistical convergence as an extension of rough convergence. We define the set of rough I-statistical limit points of a sequence and analyze the results with proofs.

On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3749-3760 ◽  
Author(s):  
Ali Karaisa ◽  
Uğur Kadak
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Bernstein Operator ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Inclusion Relations ◽  
Prior Investigation

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

Sign in / Sign up

Export Citation Format

Share Document