scholarly journals A Study of Fuzzy Sequence Spaces

2022 ◽  
Author(s):  
Vakeel A. Khan ◽  
Mobeen Ahmad ◽  
Masood Alam
Keyword(s):  
Real Number ◽  
Compact Operator ◽  
Sequence Spaces ◽  
Ideal Convergence ◽  
Inclusion Relations ◽  
Algebraic Properties ◽  
Convergence Sequence

The purpose of this chapter is to introduce and study some new ideal convergence sequence spaces FSJθT, FS0JθT and FS∞JθT on a fuzzy real number F defined by a compact operator T. We investigate algebraic properties like linearity, solidness and monotinicity with some important examples. Further, we also analyze closedness of the subspace and inclusion relations on the said spaces.

scholarly journals Some Results on Strongly Cesáro Ideal Convergent Sequence Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Mohammad Faisal Khan
Keyword(s):  
Convergent Sequence ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

Some algebraic properties of Cesáro ideal convergent sequence spaces, C I and C 0 I , are studied in this article and some inclusion relations on these spaces are established.

scholarly journals Some Generalized Difference Sequence Spaces Defined by a Sequence of Moduli inn-Normed Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Abdullah Alotaibi ◽  
Kuldip Raj ◽  
S. A. Mohiuddine
Keyword(s):  
Sequence Spaces ◽  
Infinite Matrix ◽  
Difference Sequence ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We introduce some new generalized difference sequence spaces by means of ideal convergence, infinite matrix, and a sequence of modulus functions overn-normed spaces. We also make an effort to study several properties relevant to topological, algebraic, and inclusion relations between these spaces.

scholarly journals Generalized Differenceλ-Sequence Spaces Defined by Ideal Convergence and the Musielak-Orlicz Function

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Awad A. Bakery
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Topological Properties ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
The Ideal

We introduced the ideal convergence of generalized difference sequence spaces combining an infinite matrix of complex numbers with respect toλ-sequences and the Musielak-Orlicz function overn-normed spaces. We also studied some topological properties and inclusion relations between these spaces.

scholarly journals A study of Nörlund ideal convergent sequence spaces

2020 ◽  
pp. 44-44
Author(s):  
Vakeel Khan ◽  
Sameera Abdullah ◽  
Kamal Alshlool
Keyword(s):  
Sequence Space ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Ideal Convergence ◽  
Algebraic Properties

The N?rlund matrix Nt in the theory of sequence space was firstly used by Wang. In this paper, by using the N?rlund mean Nt and the notion of ideal convergence, we introduce some new sequence spaces cI 0(Nt), cI (Nt), and `I 1(Nt) as a domain of N?rlund mean. We study some topological and algebraic properties on these spaces. Further, some inclusion concerning these spaces are discussed.

scholarly journals On Some I-Convergent Double Sequence Spaces of Fuzzy Real Numbers Defined by Modulus Function

2015 ◽  
Vol 55 (1) ◽  
pp. 19-28
Author(s):  
Manmohan Das
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Real Numbers ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties ◽  
Fuzzy Real Numbers

Abstract In this article our aim to introduce some new I-convergent double sequence spaces of fuzzy real numbers defined by modulus function and studies their some topological and algebraic properties. Also we establish some inclusion relations.

scholarly journals SOME GENERALIZED FIBONACCI DIFFERENCE SPACES DEFINED BY A SEQUENCE OF MODULUS FUNCTIONS

2017 ◽  
pp. 095 ◽  
Author(s):  
Gülsen Kılınç ◽  
Murat Candan
Keyword(s):  
Real Number ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Alpha Beta

This paper submits the sequence space $l\left( \widehat{F}\left( r,s\right),\mathcal{F},p,u\right) $ and $l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) $of non-absolute type under the domain ofthe matrix$\widehat{\text{ }F}\left( r,s\right) $ constituted by usingFibonacci sequence and non-zero real number $r$, $s$ and a sequence ofmodulus functions. We study some inclusion relations, topological andgeometric properties of these spaceses. Further, we give the $\alpha $- $%\beta $- and $\gamma $-duals of said sequence spaces and characterization ofthe classes $\left( l\left( \widehat{F}\left( r,s\right) ,\mathcal{F}%,p,u\right) ,X\right) $ and $\left( l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) ,X\right) $.

Almost strongly Orlicz double sequence spaces of regular matrices and their applications to statistical convergence

2018 ◽  
Vol 11 (05) ◽  
pp. 1850073 ◽  
Author(s):  
Kuldip Raj ◽  
Anu Choudhary ◽  
Charu Sharma
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Regular Matrix ◽  
Normed Spaces ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function over [Formula: see text]-normed spaces. We make an effort to study some topological and algebraic properties of these sequence spaces. We also study some inclusion relations between the spaces. Finally, we establish some relation between weighted lacunary statistical sequence spaces and Riesz lacunary almost statistical convergent sequence spaces over [Formula: see text]-normed spaces.

scholarly journals on ideal convergence of triple sequences in intuitionistic Fuzzy normed space defined by compact operator

2021 ◽  
Vol 40 (5) ◽  
pp. 1227-1247
Author(s):  
Vakeel A. Khan ◽  
Mohd. Imran Idrisi ◽  
Umme Tuba
Keyword(s):  
Compact Operator ◽  
Normed Space ◽  
Fuzzy Topology ◽  
Fuzzy Normed Space ◽  
Ideal Convergence ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Inclusion Relations

The main purpose of this article is to introduce and study some new spaces of I-convergence of triple sequences in intuitionistic fuzzy normed space defined by compact operator i.e 3SI (μ,ν)(T ) and 3SI0(μ,ν)(T ) and examine some fundamental properties, fuzzy topology and verify inclusion relations lying under these spaces.

scholarly journals On some spaces of Cesàro sequences of fuzzy numbers associated with λ-convergence and Orlicz function

2019 ◽  
Vol 11 (1) ◽  
pp. 156-171
Author(s):  
K. Raj ◽  
S. Pandoh
Keyword(s):  
Fuzzy Numbers ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Real Numbers ◽  
Inclusion Relations ◽  
Algebraic Properties ◽  
Fuzzy Real Numbers ◽  
Sequences Of Fuzzy Numbers

Abstract In the present paper we shall introduce some generalized difference Cesàro sequence spaces of fuzzy real numbers defined by Musielak-Orlicz function and -convergence. We make an e ort to study some topological and algebraic properties of these sequence spaces. Furthermore, some inclusion relations between these sequence spaces are establish.

scholarly journals Applications of Lacunary Sequences to Develop Fuzzy Sequence Spaces for Ideal Convergence and Orlicz Function

2020 ◽  
Vol 13 (5) ◽  
pp. 1131-1148
Author(s):  
Kuldip Raj ◽  
S. A. Mohiuddine
Keyword(s):  
Maximal Ideal ◽  
Orlicz Function ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Infinite Matrix ◽  
Ideal Convergence ◽  
Lacunary Sequences ◽  
Algebraic Properties

In the present paper, we introduce and study ideal convergence of some fuzzy sequence spaces via lacunary sequence, infinite matrix and Orlicz function. We study some topological and algebraic properties of these spaces. We also make an effort to show that these spaces are normal as well as monotone. Further, it is very interesting to show that if $I$ is not maximal ideal then these spaces are not symmetric.

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