• Title/Summary/Keyword: Space sequence

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ORLICZ SEQUENCE SPACES OF FOUR DIMENSIONAL REGULAR MATRIX AND THEIR CLOSED IDEAL

  • Raj, Kuldip;Pandoh, Suruchi;Choudhary, Anu
    • Honam Mathematical Journal
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    • v.41 no.4
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    • pp.725-744
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    • 2019
  • In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices A = (artkl). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space 𝑙2.

A NEW PARANORMED SERIES SPACE USING EULER TOTIENT MEANS AND SOME MATRIX TRANSFORMATIONS

  • Gulec, G. Canan Hazar;Ilkhan, Merve
    • Korean Journal of Mathematics
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    • v.28 no.2
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    • pp.205-221
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    • 2020
  • Paranormed spaces are important as a generalization of the normed spaces in terms of having more general properties. The aim of this study is to introduce a new paranormed space |𝜙z|(p) over the paranormed space ℓ(p) using Euler totient means, where p = (pk) is a bounded sequence of positive real numbers. Besides this, we investigate topological properties and compute the α-, β-, and γ duals of this paranormed space. Finally, we characterize the classes of infinite matrices (|𝜙z|(p), λ) and (λ, |𝜙z|(p)), where λ is any given sequence space.

INTUITIONISTIC FUZZY n-NORMED LINEAR SPACE

  • Vijayabalaji, Srinivasan;Thillaigovindan, Natesan;Jun, Young-Bae
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.2
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    • pp.291-308
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    • 2007
  • The motivation of this paper is to present a new and interesting notion of intuitionistic fuzzy n-normed linear space. Cauchy sequence and convergent sequence in intuitionistic fuzzy n-normed linear space are introduced and we provide some results onit. Furthermore we introduce generalized cartesian product of the intuitionistic fuzzy n-normed linear space and establish some of its properties.

A COMMON FIXED POINT THEOREM FOR A SEQUENCE OF MAPS IN A GENERALIZED MENGER SPACE

  • Jain, Shobha;Jain, Shishi;Bahdhur, Lal
    • East Asian mathematical journal
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    • v.24 no.4
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    • pp.359-368
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    • 2008
  • The object of this paper is to establish a unique common fixed point theorem through weak compatibility for a sequence of self-maps satisfying a generalized contractive condition in a generalized Menger space. It improves and generalizes the result of Milovanovic-Arandelovic [2], Vasuki [10] and Sehgal and Bharucha-Reid [8]. All the results presented in this paper are new.

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On the fuzzy convergence of sequences in a fuzzy normed linear space

  • Rhie, Gil-Seob;Hwang, In-Ah
    • Journal of the Korean Institute of Intelligent Systems
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    • v.18 no.2
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    • pp.268-271
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    • 2008
  • In this paper, we introduce the notions of a fuzzy convergence of sequences, fuzzy Cauchy sequence and the related fuzzy completeness on a fuzzy normed linear space. And we investigate some properties relative to fuzzy normed linear spaces. In particular, we prove an equivalent conditions that a fuzzy norm defined on a ordinary normed linear space is fuzzy complete.

ROUGH STATISTICAL CONVERGENCE IN 2-NORMED SPACES

  • Arslan, Mukaddes;Dundar, Erdinc
    • Honam Mathematical Journal
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    • v.43 no.3
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    • pp.417-431
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    • 2021
  • In this study, we introduced the notions of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained statistical convergence criteria associated with this set in 2-normed space. Then, we proved that this set is closed and convex in 2-normed space. Also, we examined the relations between the set of statistical cluster points and the set of rough statistical limit points of a sequence in 2-normed space.

ON A GENERALIZED DIFFERENCE SEQUENCE SPACES DEFINED BY A MODULUS FUNCTION AND STATISTICAL CONVERGENCE

  • Bataineh Ahmad H.A.
    • Communications of the Korean Mathematical Society
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    • v.21 no.2
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    • pp.261-272
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    • 2006
  • In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

ON ${\mathcal{I}}$-LACUNARY ARITHMETIC STATISTICAL CONVERGENCE

  • KISI, OMER
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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    • pp.327-339
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    • 2022
  • In this paper, we introduce arithmetic ${\mathcal{I}}$-statistically convergent sequence space $A{\mathcal{I}}SC$, ${\mathcal{I}}$-lacunary arithmetic statistically convergent sequence space $A{\mathcal{I}}SC_{\theta}$, strongly ${\mathcal{I}}$-lacunary arithmetic convergent sequence space $AN_{\theta}[{\mathcal{I}}]$ and prove some inclusion relations between these spaces. Futhermore, we give ${\mathcal{I}}$-lacunary arithmetic statistical continuity. Finally, we define ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-Cesàro arithmetic summability. Also, we investigate the relationship between the concepts of strongly ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-lacunary arithmetic summability and arithmetic ${\mathcal{I}}$ -statistically convergence.

SOME RESULTS ON p-DISTANCE AND SEQUENCE OF COMPLEX UNCERTAIN VARIABLES

  • Roy, Santanu;Saha, Sangeeta;Tripathy, Binod Chandra
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.907-916
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    • 2020
  • In this paper, we introduce the notion of p-distance in a complex uncertain sequence space. By using the concepts of p-distance, we give some theorems of convergence. Also, in a complex uncertain sequence space, we develope some properties on convergence in measure.

Some properties of the convergence of sequences of fuzzy points in a fuzzy normed linear space

  • Rhie, Gil-Seob;Do, Young-Uk
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.1
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    • pp.143-147
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    • 2007
  • With a new ordinary norm as an analogy of Krishna and Sarma[5] and Bag and Samanta[1], we will characterize the notions of the convergence of the sequences of fuzzy points, the fuzzy, ${\alpha}$-Cauchy sequence and fuzzy completeness.