Ideal convergent sequence spaces of fuzzy star–shaped numbers

2021 ◽  
pp. 1-8
Author(s):  
Vakeel A. Khan ◽  
Umme Tuba ◽  
SK. Ashadul Rahama ◽  
Ayaz Ahmad
Keyword(s):  
Fuzzy Sets ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Natural Numbers

In 1990, Diamond [16] primarily established the base of fuzzy star–shaped sets, an extension of fuzzy sets and numerous of its properties. In this paper, we aim to generalize the convergence induced by an ideal defined on natural numbers ℕ , introduce new sequence spaces of fuzzy star–shaped numbers in ℝ n and examine various algebraic and topological properties of the new corresponding spaces as well. In support of our results, we provide several examples of these new resulting sequences.

scholarly journals On statistical convergent sequence spaces of intuitionistic Fuzzy numbers

2018 ◽  
Vol 36 (1) ◽  
pp. 235 ◽  
Author(s):  
Shyamal Debnath ◽  
Vishnu Narayan Mishra ◽  
Jayanta Debnath
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Inclusion Relations ◽  
Bounded Sequences

In the present paper we introduce the classes of sequence stcIFN, stc0IFN and st∞IFN of statistically convergent, statistically null and statistically bounded sequences of intuitionistic fuzzy number based on the newly defined metric on the space of all intuitionistic fuzzy numbers (IFNs). We study some algebraic and topological properties of these spaces and prove some inclusion relations too.

Generalized Sequence Spaces in 2-Normed Spaces Defined by Ideal and a Modulus Function

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Sudhir Kumar ◽  
Vijay Kumar ◽  
S.S. Bhatia
Keyword(s):  
Normed Space ◽  
Difference Operator ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Topological Properties ◽  
Normed Spaces ◽  
New Class ◽  
Difference Sequences ◽  
Convergent Sequences

AbstractThe main objective of this paper is to define some new kind of generalized convergent sequence spaces with respect to a modulus function, and difference operator Δm, m ≥ 1 in a 2-normed space. We also examine some topological properties of the resulting sequence spaces. Finally, we have introduced a new class of generalized convergent sequences with the help of an ideal and difference sequences in the same space.

SOME ALMOST CONVERGENT SEQUENCE SPACES OF FUZZY NUMBERS GENERATED BY INFINITE MATRICES

2006 ◽  
Vol 02 (02) ◽  
pp. 115-121
Author(s):  
EKREM SAVAS
Keyword(s):  
Fuzzy Numbers ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Infinite Matrices ◽  
Almost Convergent Sequence ◽  
Inclusion Relations

In this paper we define some almost convergent sequence spaces of fuzzy numbers by using the A-transforms and we also examine topological properties and some inclusion relations for these new sequence spaces.

Paranorm I-convergent sequence spaces

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
Biond Tripathy ◽  
Bipan Hazarika
Keyword(s):  
Convergent Sequence ◽  
Decomposition Theorem ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Real Numbers ◽  
Positive Real ◽  
Inclusion Relations

AbstractIn this article we introduced the sequence spaces c I(p), c 0I(p), m I(p) and m 0I(p) for p = (p k), a sequence of positive real numbers. We study some algebraic and topological properties of these spaces. We prove the decomposition theorem and obtain some inclusion relations.

scholarly journals Arithmetic convergent sequence space defined by modulus function

2018 ◽  
Vol 37 (4) ◽  
pp. 129-135 ◽  
Author(s):  
Taja Yaying ◽  
Bipan Hazarika
Keyword(s):  
Sequence Space ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Topological Properties ◽  
Inclusion Results

The aim of this article is to introduce the sequence spaces $AC(f)$ and $AS(f)$ using arithmetic convergence and modulus function, and study algebraic and topological properties of this space, and certain inclusion results.

scholarly journals On Paranorm Zweier -Convergent Sequence Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vakeel A. Khan ◽  
Khalid Ebadullah ◽  
Ayhan Esi ◽  
Nazneen Khan ◽  
Mohd Shafiq
Keyword(s):  
Convergent Sequence ◽  
Decomposition Theorem ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Real Numbers ◽  
Positive Real ◽  
Inclusion Relations

In this paper, we introduce the paranorm Zweier -convergent sequence spaces , , and , a sequence of positive real numbers. We study some topological properties, prove the decomposition theorem, and study some inclusion relations on these spaces.

scholarly journals On Some Classes of Double Difference Sequences of Interval Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Kuldip Raj ◽  
Abdullah Alotaibi
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Double Difference ◽  
Difference Sequence ◽  
Topological Properties ◽  
Interval Numbers ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Interval Valued ◽  
Difference Sequence Spaces

The aim of this paper is to introduce some interval valued double difference sequence spaces by means of Musielak-Orlicz functionM=(Mij). We also determine some topological properties and inclusion relations between these double difference sequence spaces.

scholarly journals The generalized triple difference of \(\chi^{3}\) sequence spaces

2015 ◽  
Vol 3 (2) ◽  
pp. 54 ◽  
Author(s):  
N. Subramanian ◽  
Ayhan Esi
Keyword(s):  
Sequence Spaces ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Triple Difference

<p>In this paper we define some new sequence spaces and give some topological properties of the sequence spaces \(\chi^{3}\left( \Delta_{v}^{m},s, p\right)\) and \(\Lambda^{3}\left( \Delta_{v}^{m},s, p\right) \) and investigate some inclusion relations.</p>

Some Double Sequence Spaces Generated by Four-Dimensional Pascal Matrix

2021 ◽  
Vol 09 (08) ◽  
Author(s):  
Ahmadu Kiltho ◽  
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Topological Properties ◽  
Matrix Domain ◽  
Double Sequence Spaces ◽  
Pascal Matrix

The purpose of this paper is to discover and examine a four-dimensional Pascal matrix domain on Pascal sequence spaces. We show that they are spaces and also establish their Schauder basis, topological properties, isomorphism and some inclusions.

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