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.

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>

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.

scholarly journals On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Pratulananda Das ◽  
Kaustubh Dutta ◽  
Vatan Karakaya
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Statistical Cluster ◽  
Probabilistic Normed Spaces ◽  
Extremal Limit ◽  
Limit Points ◽  
Appl Math ◽  
Cluster Points

We consider the recently introduced notion ofℐ-statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509–1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826–830) in probabilistic normed spaces and in the following (Şençimen and Pehlivan (2008 vol. 26, 2008 vol. 87, 2009)) we introduce the notions like strongℐ-statistical cluster points and extremal limit points, and strongℐ-statistical continuity and strongℐ-statisticalD-boundedness in probabilistic normed spaces and study some of their important properties.

On rough convergence in amenable semigroups and some properties

2021 ◽  
pp. 1-6
Author(s):  
Erdinç Dündar ◽  
Uǧur Ulusu
Keyword(s):  
Amenable Semigroups ◽  
Limit Points ◽  
Cluster Points ◽  
Sequence Of Functions ◽  
Fixed Function

The authors of the present paper, firstly, investigated relations between the notions of rough convergence and classical convergence, and studied on some properties of the rough convergence notion which the set of rough limit points and rough cluster points of a sequence of functions defined on amenable semigroups. Then, they examined the dependence of r-limit LIMrf of a fixed function f ∈ G on varying parameter r.

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.

scholarly journals The almost lacunary $\chi^{2}$ sequence spaces defined by modulus

2014 ◽  
Vol 32 (2) ◽  
pp. 209
Author(s):  
N. Subramanian
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Modulus Function

In this paper we introduce a new concept for almost lacunary $\chi^{2}$ sequence spaces strong $P-$ convergent to zero with respect to an modulus function and examine some properties of the resulting sequence spaces. We also introduce and study statistical convergence of almost lacunary $\chi^{2}$ sequence spaces and also some inclusion theorems are discussed.

scholarly journals A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

2020 ◽  
Vol 13 (5) ◽  
pp. 1212-1230
Author(s):  
Susanta Kumar Paikray ◽  
Priyadarsini Parida ◽  
S. A. Mohiuddine
Keyword(s):  
Statistical Convergence ◽  
Type Theorem ◽  
Point Of View ◽  
Scale Function ◽  
Korovkin Type Theorem ◽  
Approximation Theorems ◽  
Fuzzy Approximation ◽  
Inclusion Relations ◽  
Korovkin Type Theorems ◽  
Sequence Of Functions

The aim of this paper is to introduce the notions of relatively deferred Nörlund uniform statistical convergence as well as relatively deferred Norlund point-wise statistical convergence through the dierence operator of fractional order of fuzzy-number-valued sequence of functions, and a type of convergence which lies between aforesaid notions, namely, relatively deferred Nörlund equi-statistical convergence. Also, we investigate the inclusion relations among these aforesaidnotions. As an application point of view, we establish a fuzzy approximation (Korovkin-type) theorem by using our new notion of relatively deferred Norlund equi-statistical convergence and intimate that this result is a non-trivial generalization of several well-established fuzzy Korovkin-type theorems which were presented in earlier works. Moreover, we estimate the fuzzy rate of the relatively deferred Nörlund equi-statistical convergence involving a non-zero scale function by using the fuzzy modulus of continuity.

SOME PROPERTIES OF EQUIDISTRIBUTED AND WELL DISTRIBUTED SEQUENCES

2021 ◽  
Vol 10 (9) ◽  
pp. 3175-3184
Author(s):  
Leila Miller-Van Wieren
Keyword(s):  
Real Numbers ◽  
Statistical Cluster ◽  
Different Types ◽  
Limit Points ◽  
Cluster Points

Many authors studied properties related to distribution and summability of sequences of real numbers. In these studies, different types of limit points of a sequence were introduced and studied including statistical and uniform statistical cluster points of a sequence. In this paper, we aim to prove some new results about the nature of different types of limit points, this time connected to equidistributed and well distributed sequences.

scholarly journals On subsequential limit points of a sequence of iterates. II

1985 ◽  
Vol 38 (1) ◽  
pp. 118-129
Author(s):  
M. Maiti ◽  
A. C. Babu
Keyword(s):  
Continuous Function ◽  
Distance Function ◽  
Metric Space ◽  
Product Space ◽  
Topological Spaces ◽  
Limit Points ◽  
Cluster Points

AbstractJ. B. Diaz and F. T. Metcalf established some results concerning the structure of the set of cluster points of a sequence of iterates of a continuous self-map of a metric space. In this paper it is shown that their conclusions remain valid if the distance function in their inequality is replaced by a continuous function on the product space. Then this idea is extended to some other mappings and to uniform and general topological spaces.

ON POINTWISE λ-STATISTICAL CONVERGENCE OF ORDER α OF SEQUENCE OF FUNCTIONS

2013 ◽  
Vol 06 (04) ◽  
pp. 1350052
Author(s):  
Mikail Et ◽  
Muhammed Çinar ◽  
Murat Karakaş
Keyword(s):  
Statistical Convergence ◽  
Sequence Of Functions

In this study, we introduce the concepts of pointwise λ-statistical convergence of order α and pointwise [V, λ]-summability of order α of sequences of real valued functions. Some relations between [Formula: see text]-statistical convergence and strong [Formula: see text]-summability are given.

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