$$\lambda _{d}$$ -Statistical Convergence, $$\lambda _{d}$$ -statistical Boundedness and Strong $$\left( V,\lambda \right) _{d}-$$ summability in Metric Spaces

2017 ◽  
pp. 391-403
Author(s):  
Emine Kayan ◽  
Rifat Çolak
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Statistical Boundedness

scholarly journals Riesz triple probabilisitic of almost lacunary ces$\acute{A}$ro $C_{111}$ statistical convergence of $\chi^{3}$ defined by a Musielak Orlicz function

2018 ◽  
Vol 36 (4) ◽  
pp. 23-32 ◽  
Author(s):  
Dr Vandana ◽  
_ Deepmala ◽  
N. Subramanian ◽  
Vishnu Narayan Mishra
Keyword(s):  
Functional Analysis ◽  
General Framework ◽  
Statistical Convergence ◽  
Metric Spaces ◽  
Orlicz Function ◽  
The Subject

In this paper we study the concept of almost lacunary statistical Ces$\acute{a}$ro of $\chi^{3}$ over probabilistic $p-$ metric spaces defined by Musielak Orlicz function. Since the study of convergence in PP-spaces is fundamental to probabilistic functional analysis, we feel that the concept of almost lacunary statistical Ces$\acute{a}$ro of $\chi^{2}$ over probabilistic $p-$ metric spaces defined by Musielak in a PP-space would provide a more general framework for the subject.

scholarly journals Statistical Convergence in Function Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Agata Caserta ◽  
Giuseppe Di Maio ◽  
Ljubiša D. R. Kočinac
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Statistical Approach ◽  
Metric Spaces ◽  
Function Spaces ◽  
Strong Uniform Convergence ◽  
Convergence Of Sequences

We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.

scholarly journals On statistical convergence in quasi-metric spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 225-236 ◽  
Author(s):  
Merve İlkhan ◽  
Emrah Evren Kara
Keyword(s):  
Functional Analysis ◽  
Computer Science ◽  
Distance Function ◽  
Metric Space ◽  
Statistical Convergence ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Applied Mathematics ◽  
Comprehensive Investigation ◽  
Cauchy Sequences

AbstractA quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric in general. Quasi-metrics are a subject of comprehensive investigation both in pure and applied mathematics in areas such as in functional analysis, topology and computer science. The main purpose of this paper is to extend the convergence and Cauchy conditions in a quasi-metric space by using the notion of asymptotic density. Furthermore, some results obtained are related to completeness, compactness and precompactness in this setting using statistically Cauchy sequences.

scholarly journals Density by Moduli and Statistical Boundedness

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Vinod K. Bhardwaj ◽  
Shweta Dhawan ◽  
Sandeep Gupta
Keyword(s):  
Statistical Convergence ◽  
Structure Theorem ◽  
Decomposition Theorem ◽  
Vector Valued ◽  
Statistical Boundedness ◽  
Bounded Sequences

We have generalized the notion of statistical boundedness by introducing the concept off-statistical boundedness for scalar sequences wherefis an unbounded modulus. It is shown that bounded sequences are precisely those sequences which aref-statistically bounded for every unbounded modulusf. A decomposition theorem forf-statistical convergence for vector valued sequences and a structure theorem forf-statistical boundedness have also been established.

scholarly journals On Kuratowski I-convergence of sequences of closed sets

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 899-912
Author(s):  
Özer Talo ◽  
Yurdal Sever
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Closed Sets ◽  
Convergence Of Sequences ◽  
Positive Integers ◽  
The Relationship ◽  
Convergent Sequences

In this paper we extend the concepts of statistical inner and outer limits (as introduced by Talo, Sever and Ba?ar) to I-inner and I-outer limits and give some I-analogue of properties of statistical inner and outer limits for sequences of closed sets in metric spaces, where I is an ideal of subsets of the set N of positive integers. We extend the concept of Kuratowski statistical convergence to Kuratowski I-convergence for a sequence of closed sets and get some properties for Kuratowski I-convergent sequences. Also, we examine the relationship between Kuratowski I-convergence and Hausdorff I-convergence.

scholarly journals Some New Observations on Wijsman ℐ 2 -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Metric Spaces ◽  
Double Sequence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Lacunary Statistical Convergence ◽  
Cesaro Convergence

In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

scholarly journals Lacunary ℐ -Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mualla Birgül Huban
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Metric Spaces ◽  
Ideal Convergence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
New Type

The concepts of invariant convergence, invariant statistical convergence, lacunary invariant convergence, and lacunary invariant statistical convergence for set sequences were introduced by Pancaroğlu and Nuray (2013). We know that ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the lacunary ℐ -invariant convergence of sequence of sets in intuitionistic fuzzy metric spaces (briefly, IFMS). In this study, we examine the notions of lacunary ℐ -invariant convergence W ℐ σ θ η , ν (Wijsman sense), lacunary ℐ ∗ -invariant convergence W ℐ σ θ ∗ η , ν (Wijsman sense), and q -strongly lacunary invariant convergence W N σ θ η , ν q (Wijsman sense) of sequences of sets in IFMS. Also, we give the relationships among Wijsman lacunary invariant convergence, W N σ θ η , ν q , W ℐ σ θ η , ν , and W ℐ σ θ ∗ η , ν in IFMS. Furthermore, we define the concepts of W ℐ σ θ η , ν -Cauchy sequence and W ℐ σ θ ∗ η , ν -Cauchy sequence of sets in IFMS. Furthermore, we obtain some features of the new type of convergences in IFMS.

scholarly journals Statistical convergence in probabilistic generalized metric spaces w.r.t. strong topology

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rasoul Abazari
Keyword(s):  
Metric Space ◽  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Metric Spaces ◽  
Asymptotic Density ◽  
Strong Topology ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Basic Facts ◽  
Definition Of

AbstractIn this paper, the concept of probabilistic g-metric space with degree l, which is a generalization of probabilistic G-metric space, is introduced. Then, by endowing strong topology, the definition of l-dimensional asymptotic density of a subset A of $\mathbb{N}^{l}$ N l is used to introduce a statistically convergent and Cauchy sequence and to study some basic facts.

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