Results 31 to 40 of about 133,611 (249)
On unitary extensions and unitary completions of topological monoids
Topological Algebra and its Applications, 2016 The concept of a unitary Cauchy net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy nets converge.
Averbukh Boris G.
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On Principal Fuzzy Metric Spaces
Mathematics, 2022 In this paper, we deal with the notion of fuzzy metric space (X,M,∗), or simply X, due to George and Veeramani. It is well known that such fuzzy metric spaces, in general, are not completable and also that there exist p-Cauchy sequences which are not ...
Valentín Gregori +3 more
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Beyond cauchy and quasi-Cauchy sequences
Filomat, 2018 In this paper, we investigate the concepts of downward continuity and upward continuity. A real valued function on a subset E of R, the set of real numbers, is downward continuous if it preserves downward quasi-Cauchy sequences; and is upward continuous if it preserves upward quasi-Cauchy sequences, where a sequence (xk) of points in R is ...
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A new study on the strongly lacunary quasi Cauchy sequences
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018 In this paper, the concept ofan -quasi-Cauchysequence is introduced. We proved interesting theorems related to -quasi-Cauchysequences. A real valued function defined on a subset of , the set of real numbers, is -ward continuous on if it preserves -quasi ...
Huseyin Cakalli, Hüseyin Kaplan
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Engineering and Technology Journal, 2011 In this paper we introduce a new definition of a fuzzy normed space (to the best of our knowledge) then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.
Jehad R. Kider
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Completeness results for metrized rings and lattices [PDF]
Categories and General Algebraic Structures with Applications, 2019 The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, $\{0\})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical
George Bergman
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A note on the nonlinear Schr\"odinger equation in a general domain
, 2018 We consider the Cauchy problem for nonlinear Schr\"odinger equations in a general domain $\Omega\subset\mathbb{R}^N$. Construction of solutions has been only done by classical compactness method in previous results.
Hayashi, Masayuki
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Deviations of ergodic sums for toral translations II. Boxes [PDF]
, 2020 We study the Kronecker sequence $\{n\alpha\}_{n\leq N}$ on the torus ${\mathbb T}^d$ when $\alpha$ is uniformly distributed on ${\mathbb T}^d.$ We show that the discrepancy of the number of visits of this sequence to a random box, normalized by $\ln^d N$,
Dolgopyat, Dmitry, Fayad, Bassam
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Real Analysis Exchange, 2005 e study $\mathcal{I}$-convergence and $\mathcal{I}$-Cauchy sequences in metric spaces where $\mathcal{I}\subset\mathcal{P}(\mathbb{N}^k)$ is an ideal containing all singletons and $k\in\{1,2\}.$$
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On Ideal Convergence in Generalized Metric Spaces
Dera Natung Government College Research Journal, 2023 Our main goal in this paper is to introduce the concept of ideal convergence in G-metric spaces. We give definitions of GI-convergence and GI*-convergence in G-metric spaces. We also extend the I-convergence concept's properties to GI-convergence.
Saime Kolancı, Mehmet Gurdal
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