I-convergence of multiple sequences in cone metric spaces

Şahiner, Ahmet; Yiğit, Tuba; Yılmaz, Nurullah

doi:10.18532/caam.99438

Cited by 3 publications

(4 citation statements)

References 23 publications

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“…This section introduces the definition for statistical (𝑀 𝜆 𝑡,𝑢,𝑣 ) summability method. Definition 2.1 [13] A complete, non-trivially valued, NAF 𝒦 is said to be an ultrametric valued field such that 1. |x|≥0 and |x|=0 if x=0; 2.…”

Section: Preliminariesmentioning

confidence: 99%

Statistical Summability for Triple Sequences over Non-Archimedean Fields

Raviselvan,

Krishnamurthy

2024

MMEP

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This paper aims to explore the concepts of statistical convergence sequence and statistical summability in non-Archimedean fields (NAF). Statistical convergence has been studied in various mathematical fields such as measure theory, probability theory, and number theory, and plays a significant role in summability theory and functional analysis. The goal of this study is to provide characterizations for triple sequences using the (𝑀 𝜆 𝑡,𝑢,𝑣 ) method of summability over NAF and to prove inclusion relations between statistical convergence and statistical (𝑀 𝜆 𝑡,𝑢,𝑣 ) summability for triple sequences over such fields. Furthermore, statistics At,u,v-summability for triple sequence has been examined in non-Archimedean fields. The non-trivially valued, complete, non-Archimedean fields are denoted by 𝒦 throughout the article.

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Section: Preliminariesmentioning

confidence: 99%

Statistical Summability for Triple Sequences over Non-Archimedean Fields

Raviselvan,

Krishnamurthy

2024

MMEP

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“…A sequence {𝑥 𝑛 } 𝑛∈ℕ in 𝑋 is said to be  * -convergent to 𝜉 ∈ 𝑋 iff there is a set Firstly, [31] introduced the concepts of triple sequences and statistically convergent triple sequences. The following definition of the extension of -convergence to triple sequences in the tvs-cms are taken from the [34] It is denoted by  3 − lim 𝑖,𝑗,𝑘→∞ 𝑥 𝑖𝑗𝑘 = 𝜉.…”

Section: Preliminariesmentioning

confidence: 99%

“…The concept of statistical convergence of sequences in real numbers was introduced in 1951 by Fast in [12]. This concept has been studied under different names (see, [2,4,5,6,8,13,24,25,29,30,33,34,35]). Cone metric spaces were actually defined by several authors many years ago and took place under different names in the literature (see, for example [1,3,7,17,21,22,23]).…”

Section: Introductionmentioning

confidence: 99%

On Quasi I-Statistical Convergence of Triple Sequences in Cone Metric Spaces

2023

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Fast [12] is credited with pioneering the field of statistical convergence. This topic has been researched in many spaces such as topological spaces, cone metric spaces, and so on (see, for example [19, 21]). A cone metric space was proposed by Huang and Zhang [17]. The primary distinction between a cone metric and a metric is that a cone metric is valued in an ordered Banach space. Li et al. [21] investigated the definitions of statistical convergence and statistical boundedness of a sequence in a cone metric space. Recently, Sakaoğlu and Yurdakadim [29] have introduced the concepts of quasi-statistical convergence. The notion of quasi I-statistical convergence for triple and multiple index sequences in cone metric spaces on topological vector spaces is introduced in this study, and we also examine certain theorems connected to quasi I-statistically convergent multiple sequences. Finally, we will provide some findings based on these theorems.

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“…Tripathy (Sahiner and Tripathy, 2008), Esi (Esi, 2014), Esi and Catalbas (Esi and Catalbas, 2014), Esi and Savas (Esi and Savas, 2015), Esi et al (Esi et al, 2016(Esi et al, , 2017a(Esi et al, , 2017b, Dutta et al (Dutta et al, 2013), Esi, 2015, 2017), Debnath et al (Debnath et al, 2015) and many others.…”

Section: Introductionmentioning

confidence: 99%

On Gradual Borel Summability Method of Rough Convergence of Triple Sequences of Beta Stancu Operators

İndumathi,

Esi,

Subramanian

2023

dngcrj

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We define the concept of rough limit set of a triple sequence space of beta Stancu operators of Borel summability of gradual real numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of beta Stancu operators of Borel summability method of gradual real numbers. Finally, we investigate some properties of the rough limit set of beta Stancu operators under which Borel summable sequence of gradual real numbers are convergent. Also, we give the results for Borel summability method of series of gradual real numbers.

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I-convergence of multiple sequences in cone metric spaces

Abstract: In this study, we introduce the ordinary and statistical convergence of double and multiple sequences in cone metric spaces. Moreover, the relationships between these convergence types are also invastigated.

Cited by 3 publications

References 23 publications

Statistical Summability for Triple Sequences over Non-Archimedean Fields

Statistical Summability for Triple Sequences over Non-Archimedean Fields

On Quasi I-Statistical Convergence of Triple Sequences in Cone Metric Spaces

On Gradual Borel Summability Method of Rough Convergence of Triple Sequences of Beta Stancu Operators

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