scholarly journals Convergence of positive series and ideal convergence

2020 ◽  
Vol 51 ◽  
Author(s):  
Vladimír Baláž ◽  
Kálmán Liptai ◽  
János Tóth T. ◽  
Tomáš Visnyai
Keyword(s):  
Ideal Convergence ◽  
Positive Series

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

Finite Difference Method on Non-Uniform Meshes for Time Fractional Diffusion Problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Haili Qiao ◽  
Aijie Cheng
Keyword(s):  
Theoretical Analysis ◽  
Fractional Derivative ◽  
Time Discretization ◽  
Summation Formula ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Initial Moment ◽  
Central Difference ◽  
Ideal Convergence ◽  
Derivative Term

AbstractIn this paper, we consider the time fractional diffusion equation with Caputo fractional derivative. Due to the singularity of the solution at the initial moment, it is difficult to achieve an ideal convergence rate when the time discretization is performed on uniform meshes. Therefore, in order to improve the convergence order, the Caputo time fractional derivative term is discretized by the {L2-1_{\sigma}} format on non-uniform meshes, with {\sigma=1-\frac{\alpha}{2}}, while the spatial derivative term is approximated by the classical central difference scheme on uniform meshes. According to the summation formula of positive integer k power, and considering {k=3,4,5}, we propose three non-uniform meshes for time discretization. Through theoretical analysis, different time convergence orders {O(N^{-\min\{k\alpha,2\}})} can be obtained, where N denotes the number of time splits. Finally, the theoretical analysis is verified by several numerical examples.

scholarly journals Ideal Convergence and Completeness of a Normed Space

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 897 ◽  
Author(s):  
Fernando León-Saavedra ◽  
Francisco Javier Pérez-Fernández ◽  
María del Pilar Romero de la Rosa ◽  
Antonio Sala
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Convergence Space ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Underlying Space ◽  
Phd Thesis

We aim to unify several results which characterize when a series is weakly unconditionally Cauchy (wuc) in terms of the completeness of a convergence space associated to the wuc series. If, additionally, the space is completed for each wuc series, then the underlying space is complete. In the process the existing proofs are simplified and some unanswered questions are solved. This research line was originated in the PhD thesis of the second author. Since then, it has been possible to characterize the completeness of a normed spaces through different convergence subspaces (which are be defined using different kinds of convergence) associated to an unconditionally Cauchy sequence.

Λ-strongly summable sequence spaces in n-normed spaces defined by ideal convergence and an Orlicz function

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Ayhan Esi ◽  
M. Kemal Özdemir
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Summable Sequence ◽  
Inclusion Results

AbstractIn this paper we introduce some certain new sequence spaces via ideal convergence, λ-sequence and an Orlicz function in n-normed spaces and study different properties of these spaces and also establish some inclusion results among them.

scholarly journals Some Results on Wijsman Ideal Convergence in Intuitionistic Fuzzy Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Ayhan Esi ◽  
Vakeel A. Khan ◽  
Mobeen Ahmad ◽  
Masood Alam
Keyword(s):  
Metric Space ◽  
Cauchy Sequence ◽  
Metric Spaces ◽  
General Setting ◽  
Fuzzy Metric Space ◽  
Ideal Convergence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Closed Sets ◽  
Intuitionistic Fuzzy

In the present work, we study and extend the notion of Wijsman J –convergence and Wijsman J ∗ –convergence for the sequence of closed sets in a more general setting, i.e., in the intuitionistic fuzzy metric spaces (briefly, IFMS). Furthermore, we also examine the concept of Wijsman J ∗ –Cauchy and J –Cauchy sequence in the intuitionistic fuzzy metric space and observe some properties.

Certain aspects of ideal convergence in topological spaces

2020 ◽  
Vol 275 ◽  
pp. 107005
Author(s):  
Pratulananda Das ◽  
Sayan Sengupta ◽  
Szymon Gła̧b ◽  
Marek Bienias
Keyword(s):  
Topological Spaces ◽  
Ideal Convergence
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