Results 41 to 50 of about 4,109,953 (303)
SOME SET THEORETIC OPERATORS PRESERVING IDEAL HAUSDORFF CONVERGENCE
, 2023 In this article, we investigate set theoretic operators preserving the ideal Hausdorff convergence of sequences of sets. Then we showed that pointwise continuous functions are not sufficient to preserve ideal Hausdorff convergence.
Olmez, Oznur +2 more
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On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence
Communications in Advanced Mathematical Sciences, 2023 In the study conducted here, we have given some new concepts in summability. In this sense, firstly, we have given the concept of lacunary $\mathcal{I}_2^{\ast}$-convergence and we have investigated the relations between lacunary $\mathcal{I}_2 ...
Nimet Pancaroğlu Akın, Erdinç Dündar
doaj +1 more source
Ideal convergence of bounded sequences
Journal of Symbolic Logic, 2007 AbstractWe generalize the Bolzano-Weierstrass theorem (that every bounded sequence of reals admits a convergent subsequence) on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to
Rafal Filipów +3 more
openaire +2 more sources
Strong Γ-ideal convergence in a probabilistic normed space
, 2016 In this paper, we investigate some properties of the set of all strong ideal cluster points of a sequence in a probabilistic normed (PN) space. We also introduce the concept of strong Gamma-ideal convergence in a PN space, and investigate some of its ...
Fulya Öztürk +2 more
semanticscholar +2 more sources
Ideal convergence and divergence of nets in $(\ell )$-groups
, 2012 summary:In this paper we introduce the ${\mathcal I}$- and ${\mathcal I}^*$-convergence and divergence of nets in $(\ell )$-groups. We prove some theorems relating different types of convergence/divergence for nets in $(\ell )$-group setting, in relation
Boccuto, Antonio +6 more
core +2 more sources
Axioms, 2021 In this survey article, we look into some recent results concerning summability matrices, both regular as well as those which are not regular (called semi-regular) and generated matrix ideals as the overall view of the inter relationship between the ...
Pratulananda Das
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$\mathcal{I}$-convergence in Fuzzy Cone Normed Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2021 The aim of this paper is to define and study the concept of $\mathcal{I}$-convergence in fuzzy cone normed space which is a generalization of R. Saadati and S. M. Vaezpour type fuzzy normal space.
Aysegul Caksu Guler
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Sets of Ideal Convergence of Sequences of Quasi-Continuous Functions
Journal of Mathematical Analysis and Applications, 2015 Tomasz Natkaniec
exaly +2 more sources
Ideal convergence generated by double summability methods
Demonstratio Mathematica, 2016 The main result of this note is that if I is an ideal generated by a regular double summability matrix summability method T that is the product of two nonnegative regular matrix methods for single sequences, then I-statistical convergence and convergence
Connor Jeff
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Ideal convergent subseries in Banach spaces [PDF]
Quaestiones Mathematicae, 2018 Assume that $\mathcal{I}$ is an ideal on $\mathbb{N}$, and $\sum_n x_n$ is a divergent series in a Banach space $X$. We study the Baire category, and the measure of the set $A(\mathcal{I}):=\left\{t \in \{0,1\}^{\mathbb{N}} \colon \sum_n t(n)x_n \textrm{ is } \mathcal{I}\textrm{-convergent}\right\}$.
Balcerzak, Marek +2 more
openaire +3 more sources