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.

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.

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>

$$\lambda $$ λ -Statistical limit points of order $$\beta $$ β of sequences of fuzzy numbers

Positivity ◽  
2014 ◽  
Vol 19 (2) ◽  
pp. 385-394
Author(s):  
A. Nihal Tuncer ◽  
Funda Babaarslan
Keyword(s):  
Fuzzy Numbers ◽  
Statistical Limit ◽  
Sequences Of Fuzzy Numbers ◽  
Limit Points

λ-Statistical limit points of the sequences of fuzzy numbers

2007 ◽  
Vol 177 (16) ◽  
pp. 3297-3304 ◽  
Author(s):  
A. Nihal Tuncer ◽  
F. Berna Benli
Keyword(s):  
Fuzzy Numbers ◽  
Statistical Limit ◽  
Sequences Of Fuzzy Numbers ◽  
Limit Points

scholarly journals On the almost everywhere statistical convergence of sequences of fuzzy numbers

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2683-2693 ◽  
Author(s):  
Özer Talo
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Almost Everywhere ◽  
Statistical Limit ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

In this paper, we define the concept of almost everywhere statistical convergence of a sequence of fuzzy numbers and prove that a sequence of fuzzy numbers is almost everywhere statistically convergent if and only if its statistical limit inferior and limit superior are equal. To achieve this result, new representations for statistical limit inferior and limit superior of a sequence of fuzzy numbers are obtained and we show that some properties of statistical limit inferior and limit superior can be easily derived from these representations.

scholarly journals $\mu$-statistical convergence and the space of functions $\mu$-stat continuous on the segment

2021 ◽  
Vol 13 (2) ◽  
pp. 433-451
Author(s):  
S.R. Sadigova
Keyword(s):  
Banach Space ◽  
Borel Measure ◽  
Statistical Convergence ◽  
Continuous Functions ◽  
Statistical Limit ◽  
The Relationship

In this work, the concept of a point $\mu$-statistical density is defined. Basing on this notion, the concept of $\mu$-statistical limit, generated by some Borel measure $\mu\left(\cdot \right)$, is defined at a point. We also introduce the concept of $\mu$-statistical fundamentality at a point, and prove its equivalence to the concept of $\mu$-stat convergence. The classification of discontinuity points is transferred to this case. The appropriate space of $\mu$-stat continuous functions on the segment with sup-norm is defined. It is proved that this space is a Banach space and the relationship between this space and the spaces of continuous and Lebesgue summable functions is considered.

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.

On New Difference Sequence Space and Their Generalised Almost Statistical Convergence

2020 ◽  
pp. 212-219
Author(s):  
Ajaya Kumar Singh
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Convergent Sequence ◽  
Difference Sequence ◽  
Almost Convergence ◽  
Topological Properties ◽  
Statistical Limit ◽  
Difference Sequence Space ◽  
Limit Functional ◽  
Convergent Sequences

The object of the present paper is to introduce the notion of generalised almost statistical (GAS) convergence of bounded real sequences, which generalises the notion of almost convergence as well as statistical convergence of bounded real sequences. We also introduce the concept of Banach statistical limit functional and the notion of GAS convergence mainly depends on the existence of Banach statistical limit functional. We prove the existence of Banach statistical limit functional. Also, the existence GAS convergent sequence, which is neither statistical convergent nor almost convergent. Lastly, some topological properties of the space of all GAS convergent sequences are investigated.

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