scholarly journals A new type of difference I-convergent sequence in IFnNS

2021 ◽  
pp. 22-22
Author(s):  
Vakeel Khan ◽  
Izhar Khan ◽  
Mobeen Ahmad
Keyword(s):  
Cauchy Sequence ◽  
Convergent Sequence ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
New Type

In this paper, we introduce the notion of a generalized difference I-convergent (i.e.?m-I-convergent) and difference I-Cauchy (i.e.?m-I-Cauchy) sequence in intuitionistic fuzzy n-normed spaces. Further, we prove some results related to this notion. Also, we study the concepts of a generalized difference I+-convergent (i.e.?m-I+-convergent) sequence in intuitionistic fuzzy n-normed spaces and show the relation between them.

scholarly journals Lacunary ℐ -Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mualla Birgül Huban
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Metric Spaces ◽  
Ideal Convergence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
New Type

The concepts of invariant convergence, invariant statistical convergence, lacunary invariant convergence, and lacunary invariant statistical convergence for set sequences were introduced by Pancaroğlu and Nuray (2013). We know that ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the lacunary ℐ -invariant convergence of sequence of sets in intuitionistic fuzzy metric spaces (briefly, IFMS). In this study, we examine the notions of lacunary ℐ -invariant convergence W ℐ σ θ η , ν (Wijsman sense), lacunary ℐ ∗ -invariant convergence W ℐ σ θ ∗ η , ν (Wijsman sense), and q -strongly lacunary invariant convergence W N σ θ η , ν q (Wijsman sense) of sequences of sets in IFMS. Also, we give the relationships among Wijsman lacunary invariant convergence, W N σ θ η , ν q , W ℐ σ θ η , ν , and W ℐ σ θ ∗ η , ν in IFMS. Furthermore, we define the concepts of W ℐ σ θ η , ν -Cauchy sequence and W ℐ σ θ ∗ η , ν -Cauchy sequence of sets in IFMS. Furthermore, we obtain some features of the new type of convergences in IFMS.

scholarly journals -Ward Continuity

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Huseyin Cakalli
Keyword(s):  
Cauchy Sequence ◽  
Convergent Sequence ◽  
Lacunary Sequence ◽  
Real Numbers ◽  
Cauchy Sequences ◽  
New Type ◽  
Positive Integers ◽  
Convergent Sequences

A function is continuous if and only if preserves convergent sequences; that is, is a convergent sequence whenever is convergent. The concept of -ward continuity is defined in the sense that a function is -ward continuous if it preserves -quasi-Cauchy sequences; that is, is an -quasi-Cauchy sequence whenever is -quasi-Cauchy. A sequence of points in , the set of real numbers, is -quasi-Cauchy if , where , and is a lacunary sequence, that is, an increasing sequence of positive integers such that and . A new type compactness, namely, -ward compactness, is also, defined and some new results related to this kind of compactness are obtained.

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.

Star Neutrosophic Fuzzy Topological Space

2020 ◽  
pp. 77-82
Author(s):  
A.A A.A.Salama ◽  
◽  
◽  
◽  
Hewayda ElGhawalby ◽  
...  
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
New Type

In this paper, we aim to develop a new type of neutrosophic fuzzy set called the star neutrosophic fuzzy set as a generalization to star neutrosophic crisp set defined in by Salama et al.[8], and study some of its properties. Adedd to, we introduce the notion of star neutrosophic fuzzy topological space as a generalization to some topological consepts as star neutrosophic fuzzy closure, and star neutrosophic fuzzy interior. Finally, we extend the concepts of fuzzy topological space, and intuitionistic fuzzy topological space to the case of star neutrosophic fuzzy sets.

scholarly journals Strongly Lacunary Ward Continuity in 2-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hüseyin Çakalli ◽  
Sibel Ersan
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Cauchy Sequences

A functionfdefined on a subsetEof a 2-normed spaceXis strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points inE; that is,(f(xk))is a strongly lacunary quasi-Cauchy sequence whenever (xk) is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in 2-normed spaces.

Matrix Transformations in an Incomplete Space

1968 ◽  
Vol 20 ◽  
pp. 727-734 ◽  
Author(s):  
I. J. Maddox
Keyword(s):  
Linear Space ◽  
Cauchy Sequence ◽  
Convergent Sequence ◽  
Convergent Series ◽  
Matrix Transformations ◽  
Cauchy Sequences ◽  
Complex Linear ◽  
Incomplete Space ◽  
Bounded Sequences ◽  
Convergent Sequences

Let X = (X, p) be a seminormed complex linear space with zero θ. Natural definitions of convergent sequence, Cauchy sequence, absolutely convergent series, etc., can be given in terms of the seminorm p. Let us write C = C(X) for the set of all convergent sequences for the set of Cauchy sequences; and L∞ for the set of all bounded sequences.

scholarly journals New Fuzzy Normed Spaces

2012 ◽  
Vol 9 (3) ◽  
pp. 559-564 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Continuous Convergence ◽  
Definition Of

In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.

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