<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="script">I</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="script">K</mml:mi></mml:mrow></mml:msup></mml:math>-Cauchy functions

Das, Pratulananda; Sleziak, Martin; Toma, Vladimír

doi:10.1016/j.topol.2014.05.008

Cited by 12 publications

(10 citation statements)

References 17 publications

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“…They also gave the condition AP(I, K) modifying condition AP from [9,17]. Later in the year 2014, I K -Cauchy and I K -Cauchy net have been studied in [10,21].…”

Section: Et Al the Results Is As Followsmentioning

confidence: 99%

A Note on I^K and I^K*-convergence in topological spaces

Banerjee¹,

Paul²

2018

Preprint

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“…They also gave the condition AP(I, K) modifying condition AP from [9,17]. Later in the year 2014, I K -Cauchy and I K -Cauchy net have been studied in [10,21].…”

Section: Et Al the Results Is As Followsmentioning

confidence: 99%

A Note on I^K and I^K*-convergence in topological spaces

Banerjee¹,

Paul²

2018

Preprint

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“…So from that point of view the concept of I K -convergence being an extension of I * -convergence shows a strong analogy for further investigation. Recent developments in the direction of I K -convergence from topological aspects can be found from the works of Das et al [4,5], Banerjee and Paul [2,3] and many others.…”

Section: Introductionmentioning

confidence: 99%

ON \(A^{\mathcal{I^{K}}}\)–SUMMABILITY

Choudhury

Debnath

2022

UMJ

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In this paper, we introduce and investigate the concept of \(A^{\mathcal{I^{K}}}\)-summability as an extension of \(A^{\mathcal{I^{*}}}\)-summability which was recently (2021) introduced by O.H.H.~Edely, where \(A=(a_{nk})_{n,k=1}^{\infty}\) is a non-negative regular matrix and \(\mathcal{I}\) and \(\mathcal{K}\) represent two non-trivial admissible ideals in \(\mathbb{N}\). We study some of its fundamental properties as well as a few inclusion relationships with some other known summability methods. We prove that \(A^{\mathcal{K}}\)-summability always implies \(A^{\mathcal{I^{K}}}\)-summability whereas \(A^{\mathcal{I}}\)-summability not necessarily implies \(A^{\mathcal{I^{K}}}\)-summability. Finally, we give a condition namely \(AP(\mathcal{I},\mathcal{K})\) (which is a natural generalization of the condition \(AP\)) under which \(A^{\mathcal{I}}\)-summability implies \(A^{\mathcal{I^{K}}}\)-summability.

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“…Comparisons of I K -convergence with I-convergence [11] can be found in [1,6,8]. A few articles for example [9,7] contributed to the study of I K -convergence of sequence of functions. Some of the definitions and results of [3,6] that are used in subsequent sections are listed below.…”

Section: Introductionmentioning

confidence: 99%

Further aspects of I K-convergence in topological spaces

Sharmah

Hazarika

2021

Appl. Gen. Topol.

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In this paper, we obtain some results on the relationships between different ideal convergence modes namely, I K, I K∗ , I, K, I ∪ K and (I ∪K) ∗ . We introduce a topological space namely I K-sequential space and show that the class of I K-sequential spaces contain the sequential spaces. Further I K-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space X, we characterize the set of I K-cluster points of the sequence as closed subsets of X.

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IK-Cauchy functions

Cited by 12 publications

References 17 publications

A Note on I^K and I^K*-convergence in topological spaces

A Note on I^K and I^K*-convergence in topological spaces

ON \(A^{\mathcal{I^{K}}}\)–SUMMABILITY

Further aspects of I K-convergence in topological spaces

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