scholarly journals Ideal convergent sequence and ideal Cauchy sequence of functions in two normed spaces over ultrametric fields

2020 ◽  
Author(s):  
S. Sangeetha ◽  
K. Suja
Keyword(s):  
Cauchy Sequence ◽  
Convergent Sequence ◽  
Normed Spaces ◽  
Sequence Of Functions

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 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.

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.

scholarly journals Some Almost Lacunary Double Sequence Spaces Defined by Orlicz Functions in 2-Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Orhan Tug
Keyword(s):  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Normed Spaces ◽  
Orlicz Functions ◽  
Double Sequence Spaces ◽  
Almost Convergent Sequence

Das and Patel (1989) introduced two new sequence spaces which are called lacunary almost convergent and lacunary strongly almost convergent sequence spaces. Móricz and Rhoades (1988) defined and studied almost P-convergent double sequences spaces. Savaş and Patterson (2005) introduce the almost lacunary strong P-convergent double sequence spaces by using Orlicz functions and examined some properties of these sequences spaces. In this paper, some almost lacunary double sequences spaces are given by using 2-normed spaces.

scholarly journals Ideally Statistical Convergence in n-normed Space

2020 ◽  
pp. 75-84
Author(s):  
Nazneen Khan ◽  
Amani Shatarah
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Topological Properties ◽  
Normed Spaces

The aim of the article is to extend the concept of Ideally statistical convergence from 2 normed spaces to n-normed space. We have also study and prove some important algebraic and topological properties of Ideally-statistical convergence of real sequences in n-normed space. In the last part of this article we obtain a criterion for I-statistically Cauchy sequence in n-normed space to be I-statistically Cauchy with respect to ∥.∥∞.

scholarly journals Complete Fuzzy n-normed linear space

2014 ◽  
Vol 3 (1) ◽  
Author(s):  
S. Vijayabalaji ◽  
N. Thillaigovindan
Keyword(s):  
Linear Space ◽  
Cauchy Sequence ◽  
Normed Linear Space ◽  
Convergent Sequence ◽  
Subject Classification

This paper introduces the notion of Cauchy sequence, convergent sequence and completeness in fuzzy n-normed linear space. AMS Mathematics Subject Classification: 46S40, 03E72.

scholarly journals Asymptotic Behavior of Resolvents of a Convergent Sequence of Convex Functions on Complete Geodesic Spaces

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 21
Author(s):  
Yasunori Kimura ◽  
Keisuke Shindo
Keyword(s):  
Asymptotic Behavior ◽  
Convex Functions ◽  
Lower Semicontinuous ◽  
Convergent Sequence ◽  
Lower Semicontinuous Function ◽  
Semicontinuous Function ◽  
Geodesic Space ◽  
Proper Convex ◽  
Convex Lower Semicontinuous Function ◽  
Sequence Of Functions

The asymptotic behavior of resolvents of a proper convex lower semicontinuous function is studied in the various settings of spaces. In this paper, we consider the asymptotic behavior of the resolvents of a sequence of functions defined in a complete geodesic space. To obtain the result, we assume the Mosco convergence of the sets of minimizers of these functions.

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