On The Quadruple Sequence Spaces of Fuzzy Complex Numbers

2021 ◽  
Vol 26 (5) ◽  
pp. 58-65
Author(s):  
Aqeel Hussein
Keyword(s):  
Sequence Spaces ◽  
Complex Numbers

           In this paper, the quadruple sequence spaces of fuzzy complex numbers are shown, and several features such as solidity, symmetry, monotonicity, and convergence-free are discussed. 

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 Strongly almost convergent generalized difference sequences associated with multiplier sequences

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Ayhan Esi ◽  
Binod Tripathy
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Difference Sequence ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Convergent Sequences

AbstractLet Λ = (λk) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference sequence spaces associated with multiplier sequences i.e. w 0[A,Δm,Λ,p], w 1[A,Λm,Λ,p], w ∞[A,Δm,Λ,p] and study their different properties. We also introduce ΔΛm-statistically convergent sequences and give some inclusion relations between w 1[Δm,λ,p] convergence and ΔΛm-statistical convergence.

scholarly journals Matrix transformations of some sequence spaces—II

1970 ◽  
Vol 11 (2) ◽  
pp. 162-166 ◽  
Author(s):  
K. Chandrasekhara Rao
Keyword(s):  
Vector Space ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Complex Numbers ◽  
Image Position

This paper is a continuation of [1]. We begin with the notations for the sequence spaces considered in this paper. Let Γ be the space of sequences x = {xp} of complex numbers such that |xp|1/p⃗0 as p⃗∞. Γ can also be regarded as the space of integral functions f(z) = . The sequence space Γ is a vector space over the complex numbers with seminorms

scholarly journals A Class of Sequences Defined by Weak Ideal Convergence and Musielak-Orlicz Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Awad A. Bakery
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Topological Properties ◽  
Inclusion Relation ◽  
Normed Spaces ◽  
Ideal Convergence

We introduced the weak ideal convergence of new sequence spaces combining an infinite matrix of complex numbers and Musielak-Orlicz function over normed spaces. We also study some topological properties and inclusion relation between these spaces.

scholarly journals Cesàro Summable Sequence Spaces over the Non-Newtonian Complex Field

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Uğur Kadak
Keyword(s):  
Sequence Spaces ◽  
Matrix Transformations ◽  
Complex Numbers ◽  
Complex Field ◽  
Cesàro Summability ◽  
Summable Sequence ◽  
Cesaro Summability ◽  
Cesàro Method

The spacesω0p,ωp, andω∞pcan be considered the sets of all sequences that are strongly summable to zero, strongly summable, and bounded, by the Cesàro method of order1with indexp. Here we define the sets of sequences which are related to strong Cesàro summability over the non-Newtonian complex field by using two generator functions. Also we determine theβ-duals of the new spaces and characterize matrix transformations on them into the sets of⁎-bounded,⁎-convergent, and⁎-null sequences of non-Newtonian complex numbers.

scholarly journals Some New Lacunary Strong Convergent Vector-Valued Sequence Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
M. Mursaleen ◽  
A. Alotaibi ◽  
Sunil K. Sharma
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Vector Valued

We introduce some vector-valued sequence spaces defined by a Musielak-Orlicz function and the concepts of lacunary convergence and strong (A)-convergence, whereA=(aik)is an infinite matrix of complex numbers. We also make an effort to study some topological properties and some inclusion relations between these spaces.

On topological sequence spaces

1967 ◽  
Vol 63 (4) ◽  
pp. 997-1019 ◽  
Author(s):  
D. J. H. Garling
Keyword(s):  
Boolean Algebra ◽  
Sequence Space ◽  
Linear Subspace ◽  
Sequence Spaces ◽  
Vector Spaces ◽  
Order Structure ◽  
Complex Numbers ◽  
Vector Valued ◽  
Considerable Detail ◽  
Partially Ordered Spaces

We denote by ω the linear space of all sequences of real or complex numbers. A linear subspace of ω is called a sequence space. A subset A of ω is solid if whenever x ∈ A and |yi| ≤ |xi| for each i, then y ∈ A. The theory of solid sequence spaces, topologized in a variety of ways, has been developed in considerable detail, in particular by Köthe and Toeplitz (13) and subsequently by Köthe (see, for example (12)). These results have been generalized to function spaces by Dieudonné(6), to vector-valued sequence spaces by Pietsch (18), to vector spaces with a Boolean algebra of projections by Cooper ((4), (5)), and in the real case, to partially-ordered spaces by Luxemburg and Zaanen (see, for example (14)) and Fremlin (8). This last generalization shows that many of the properties of solid sequence spaces depend upon their order structure, rather than upon their structure as sequence spaces.

STRONGLY (VΛ,A,P) - SUMMABLE SEQUENCE SPACES DEFINED BY A MODULUS

2007 ◽  
Vol 12 (4) ◽  
pp. 419-424 ◽  
Author(s):  
Tunay Bilgin ◽  
Yilmaz Altun
Keyword(s):  
Key Words ◽  
Statistical Convergence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Real Numbers ◽  
Positive Real ◽  
Summable Sequence ◽  
De La Vallée Poussin

We introduce the strongly (Vλ,A,p) ‐ summable sequences and give the relation between the spaces of strongly (Vλ,A,p) ‐ summable sequences and strongly (Vλ,A,p) ‐ summable sequences with respect to a modulus function when A = (α ik ) is an infinite matrix of complex numbers and ρ = (pi) is a sequence of positive real numbers. Also we give natural relationship between strongly (Vλ, A,p) ‐ convergence with respect to a modulus function and strongly Sλ (A) ‐ statistical convergence. Key words: De la Vallee‐Poussin mean, modulus function, statistical convergence.

Maximum Modulus Theorems and Schwarz Lemmata for Sequence Spaces, II

1978 ◽  
Vol 21 (1) ◽  
pp. 79-84
Author(s):  
B. L. R. Shawyer
Keyword(s):  
Sequence Space ◽  
Maximum Modulus ◽  
Maximal Functions ◽  
Sequence Spaces ◽  
Schwarz Lemma ◽  
Complex Numbers ◽  
Maximum Modulus Theorem ◽  
The Schwarz Lemma

In this note, we continue the investigations of [3], proving another analogue of the maximum modulus theorem, this time for the sequence space bv, and we investigate maximal functions for such theorems. As in [3], we use the notation f∈MM if f is analytic in the disk |z| <1, continuous for |z| ≤ 1 and satisfies |f(z)| ≤ 1 on |z| = 1. We also write f∈SL if f∈MM and f(0) = 0. Whenever x={xk} is a sequence of complex numbers, we write f(x) = {f(xk)}.In [3], we proved analogues of the maximum modulus theorem for the sequence spaces 5, m and c, and analogues of the Schwarz Lemma for the sequence spaces c0, lp and bv0. We begin this note with the sequence space bv.

scholarly journals Lacunary strong convergence of difference sequences with respect to a modulus function

Filomat ◽  
2003 ◽  
pp. 9-14 ◽  
Author(s):  
Rifat Colak
Keyword(s):  
Positive Integer ◽  
Strong Convergence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Complex Numbers ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Fixed Positive Integer ◽  
Positive Integers

A sequence ? = (kr) of positive integers is called lacunary if k0 = 0, 0 < kr < kr+1 and hr = kr ? kr-1 ? ? as r ? ?. The intervals determined by ? are denoted by Ir = (kr-1, kr]. Let ? be the set of all sequences of complex numbers and f be a modulus function. Then we define N?(?m, f) = {x ? ?: lim 1/hr ? f(|?m xk -l|)=0 for some l} r k?Ir N?0(?m, f) = {x ? ?: lim 1/hr ? f(|?m xk|)=0} r k?Ir N??(?m, f) = {x ? ?: sup 1/hr ? f(|?m xk|)< ?} r k?Ir where ?xk = xk - xk+1, ?mxk = ?m-1xk - ?m-1xk+1 and m is a fixed positive integer. In this study we give various properties and inclusion relations on these sequence spaces.

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