scholarly journals On rough convergence in 2-normed spaces and some properties

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5077-5086
Author(s):  
Mukaddes Arslan ◽  
Erdinç Dündar
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Fixed Sequence ◽  
Limit Points ◽  
Cluster Points

In this study, we investigated relationships between rough convergence and classical convergence and studied some properties about the notion of rough convergence, the set of rough limit points and rough cluster points of a sequence in 2-normed space. Also, we examined the dependence of r-limit LIMr 2xn of a fixed sequence (xn) on varying parameter r in 2-normed space

scholarly journals On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Normed Space ◽  
Complex Numbers ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Cauchy Sequences ◽  
Limit Points ◽  
Positive Integers ◽  
Cluster Points

An idealIis a hereditary and additive family of subsets of positive integersℕ. In this paper, we will introduce the concept of generalized randomn-normed space as an extension of randomn-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence andL-ideal Cauchy for sequences of complex numbers in the generalized randomn-norm. We introduceIL-limit points andIL-cluster points. Furthermore, Cauchy andIL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.

scholarly journals Lacunary Statistical Limit Points in Random 2-Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
A. Güncan ◽  
U. Yamancı ◽  
M. Gürdal
Keyword(s):  
Normed Spaces ◽  
Statistical Limit ◽  
Limit Points ◽  
Cluster Points

We introduce the notion θ-cluster points, investigate the relation between θ-cluster points and limit points of sequences in the topology induced by random 2-normed spaces, and prove some important results.

scholarly journals On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Pratulananda Das ◽  
Kaustubh Dutta ◽  
Vatan Karakaya
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Statistical Cluster ◽  
Probabilistic Normed Spaces ◽  
Extremal Limit ◽  
Limit Points ◽  
Appl Math ◽  
Cluster Points

We consider the recently introduced notion ofℐ-statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509–1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826–830) in probabilistic normed spaces and in the following (Şençimen and Pehlivan (2008 vol. 26, 2008 vol. 87, 2009)) we introduce the notions like strongℐ-statistical cluster points and extremal limit points, and strongℐ-statistical continuity and strongℐ-statisticalD-boundedness in probabilistic normed spaces and study some of their important properties.

On ideal convergence in probabilistic normed spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
M. Mursaleen ◽  
S. Mohiuddine
Keyword(s):  
Normed Space ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Probabilistic Normed Space ◽  
Ideal Convergence ◽  
Probabilistic Normed Spaces ◽  
Real Anal ◽  
The Relationship ◽  
Cluster Points ◽  
Interesting Generalization

AbstractAn interesting generalization of statistical convergence is I-convergence which was introduced by P.Kostyrko et al [KOSTYRKO,P.—ŠALÁT,T.—WILCZYŃSKI,W.: I-Convergence, Real Anal. Exchange 26 (2000–2001), 669–686]. In this paper, we define and study the concept of I-convergence, I*-convergence, I-limit points and I-cluster points in probabilistic normed space. We discuss the relationship between I-convergence and I*-convergence, i.e. we show that I*-convergence implies the I-convergence in probabilistic normed space. Furthermore, we have also demonstrated through an example that, in general, I-convergence does not imply I*-convergence in probabilistic normed space.

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.

Some sequence spaces and completeness of normed spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 281-287
Author(s):  
RAMAZAN KAMA ◽  
◽  
BILAL ALTAY ◽  
Keyword(s):  
Normed Space ◽  
Summability Method ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Cesàro Summability ◽  
Cesaro Summability

In this paper we introduce new sequence spaces obtained by series in normed spaces and Cesaro summability method. We prove that completeness ´ and barrelledness of a normed space can be characterized by means of these sequence spaces. Also we establish some inclusion relationships associated with the aforementioned sequence spaces.

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.

scholarly journals Isometries of ultrametric normed spaces

2021 ◽  
Vol 12 (4) ◽  
Author(s):  
Javier Cabello Sánchez ◽  
José Navarro Garmendia
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Tingley’S Problem ◽  
Group Of Isometries

AbstractWe show that the group of isometries of an ultrametric normed space can be seen as a kind of a fractal. Then, we apply this description to study ultrametric counterparts of some classical problems in Archimedean analysis, such as the so called Problème des rotations de Mazur or Tingley’s problem. In particular, it turns out that, in contrast with the case of real normed spaces, isometries between ultrametric normed spaces can be very far from being linear.

scholarly journals Some properties of the superior and inferior semi inner product function associated to the 2-norm

2016 ◽  
Vol 12 (5) ◽  
pp. 6254-6260
Author(s):  
Stela Ceno
Keyword(s):  
Normed Space ◽  
Scalar Product ◽  
Inner Product ◽  
Normed Spaces ◽  
Close Link ◽  
Long Period ◽  
Product Function

Special properties that the scalar product enjoys and its close link with the norm function have raised the interest of researchers from a very long period of time. S.S. Dragomir  presents concrete generalizations of the scalar product functions  in a normed space and deals with the interesting properties of them. Based on S.S. Dragomirs idea in this paper we treat generalizations of superior and inferior scalar product functions in the case of semi-normed spaces and 2-normed spaces.

Sign in / Sign up

Export Citation Format

Share Document