I - convergence on cone metric spaces

Pal, Sudip Kumar; Savaş, Ekrem; Cakalli, Huseyin

doi:10.5644/sjm.09.1.07

Cited by 22 publications

(1 citation statement)

References 19 publications

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“…The idea of statistical convergence has been further extended to -convergence in [19] using the notion of ideals of natural numbers, with many interesting consequences. Further investigations in this direction and more applications of ideals can be found in [10,16,27,28]. In another direction, a new type of convergence was introduced in [11] called -statistical convergence.…”

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

2023

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Lacunary Statistically Slowly Oscillating Continuity in Abstract Spaces

Hazarika

2017

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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A Variation on Statistical Ward Continuity

Cakalli

2015

Bull. Malays. Math. Sci. Soc.

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A real valued function defined on a subset E of R, the set of real numbers, is ρ-statistically downward continuous if it preserves ρ-statistical downward quasi-Cauchy sequences of points in E, where a sequence (α k ) of real numbers is called ρ-statistically downward quasi-Cauchy if limn→∞ 1 ρn |{k ≤ n : ∆α k ≥ ε}| = 0 for every ε > 0, in which (ρn) is a non-decreasing sequence of positive real numbers tending to ∞ such that lim sup n ρn n < ∞, ∆ρn = O(1), and ∆α k = α k+1 − α k for each positive integer k. It turns out that a function is uniformly continuous if it is ρ-statistical downward continuous on an above bounded set. 1 hr k∈Ir |α k − L| = 0, where I r = (k r−1 , k r ], and k 0 = 0, h r := k r − k r−1 → ∞ as r → ∞ and θ = (k r )is an increasing sequence of positive integers (see also [45], and [46]). In [43] Fridy and Orhan introduced the concept of lacunary statistically convergence in the sense that a sequence (α k ) of points in R is called lacunary statistically convergent, or Date: September 27, 2018. 2010 Mathematics Subject Classification. Primary: 40A05; Secondaries: 40D25; 40A35; 40A30; 26A15.

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I - convergence on cone metric spaces

Cited by 22 publications

References 19 publications

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

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

Lacunary Statistically Slowly Oscillating Continuity in Abstract Spaces

A Variation on Statistical Ward Continuity

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