On statistical convergence in cone metric spaces

Ke-dian, LI; Lin, Shou; Ge, Ying

doi:10.1016/j.topol.2015.05.038

Cited by 13 publications

(9 citation statements)

References 15 publications

(13 reference statements)

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“…Equivalency in the following theorem has been studied for cone metric space in [13], now we prove it on g-metric space.…”

Section: And Denoted By; Gsmentioning

confidence: 90%

Statistical convergence in g-metric spaces

Abazari¹

2021

Preprint

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The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.Definition 1.1. [14] Let X be a nonempty set and Let G : X × X × X → R + , be a function satisfying: 1) G(x, y, z) = 0 if x = y = z, 2) 0 < G(x, x, y); for all x, y ∈ X , with x = y, 3) G(x, x, y) G(x, y, z) , for all x, y, z ∈ X with z = y, 4) G(x, y, z) = G(x, z, y) = G(y, z, x) = ... , (symmetry in all three variables),

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“…Equivalency in the following theorem has been studied for cone metric space in [13], now we prove it on g-metric space.…”

Section: And Denoted By; Gsmentioning

confidence: 90%

Statistical convergence in g-metric spaces

Abazari¹

2021

Preprint

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“…Equivalency in the following theorem has been studied for cone metric space in [13], now we prove it on -metric space.…”

Section: Definition 28mentioning

confidence: 91%

Statistical convergence in g-metric spaces

Abazari

2022

Filomat

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“…So in (1951), Fast [3] and Steinhaus [4], introduced the idea of (Statistical Convergence for Sequences), as a result the statistical convergence has several applications indifferent fields of mathematics some of these fields, including topology [5,6] and fuzzy analysis [7,8,9,10]. So separately from some basic, and main properties of this notion was studied by, buck [11], Salàt [12], Shoenberg [13].The concept of "fuzzy norm" was presented by Katsaras [14].…”

Section: Introductionmentioning

confidence: 99%

On Fuzzy Statistical (O)-Convergence in Fuzzy Riesz Spaces

Kadhim

2020

ANJS

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In this paper, we present the concepts of fuzzy order convergence, fuzzy statistical (O)-Convergence (Fso-Convergence), and fuzzy statistical Cauchy sequence in fuzzy Riesz spaces, their fundamental properties are established, some important theorems are given, and show every (Fso-Convergence) can be fuzzy statistical Cauchy and prove that any one of two sequences is fuzzy order converge leads to the second sequence is fuzzy statistical (O)-Convergence. In addition, we have also demonstrated through examples that, in general, "fuzzy ordered linear space, need not to be a fuzzy Riesz spaces".

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On statistical convergence in cone metric spaces

Cited by 13 publications

References 15 publications

Statistical convergence in g-metric spaces

Statistical convergence in g-metric spaces

Statistical convergence in g-metric spaces

On Fuzzy Statistical (O)-Convergence in Fuzzy Riesz Spaces

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