A NEW SEQUENCE SPACE DEFINED BY A MODULUS (original) (raw)

On a class of generalized difference sequence space definedby modulus function

Hokkaido mathematical journal, 2005

In this article we introduce the sequence space m(f, φ, ∆ n , p, q), 1 ≤ p < ∞, using modulus functions. We study its different properties like completeness, solidity etc. Also we obtain some inclusion results involving the space m(f, φ, ∆ n , p, q).

On generalized sequence spaces via modulus function

Journal of Inequalities and Applications, 2014

In this paper, we introduce and study the concept of lacunary strongly (A, ϕ)-convergence with respect to a modulus function and lacunary (A, ϕ)-statistical convergence and examine some properties of these sequence spaces. We establish some connections between lacunary strongly (A, ϕ)-convergence and lacunary (A, ϕ)-statistical convergence.

A new generalized vector-valued paranormed sequence space using modulus function

In this paper we introduce a new generalized vector-valued paranormed sequence spaces N p (E k , m u , f , s) using modulus function f , where p = (p k ) is a bounded sequence of positive real numbers such that inf k p k > 0, (E k , q k ) is a sequence of seminormed spaces with E k+1 ⊆ E k for each k ∈ N and s ≥ 0. We prove results regarding completeness, K-space, normality, inclusion relation are derived. These are more general than those of Ruckle [7], Maddox [5], Ozturk and Bilgin [6], Sahiner [8], Atlin et al. [1] and Srivastava and Kumar [9].

Double sequence spaces defined by a modulus

Mathematica Slovaca, 2011

This paper begins with new definitions for double sequence spaces. These new definitions are constructed, in general, by combining modulus function and nonnegative four-dimensional matrix. We use these definitions to establish inclusion theorems between various sequence spaces such as: If A = (a m,n,k,l ) be a nonnegative four-dimensional matrix such that mathopsuplimitsm,nsumlimitsk,l=0,0infty,inftyam,n,k,l<infty\mathop {\sup }\limits_{m,n} \sum\limits_{k,l = 0,0}^{\infty ,\infty } {a_{m,n,k,l} < \infty }mathopsuplimitsm,nsumlimitsk,l=0,0infty,inftyam,n,k,l<infty and let f be a modulus, then ω″(A, f) ⊂ ω″∞(A, f) and ω″0(A, f) ⊂ ω″∞(A, f).

Some New Type of Multiplier Sequence Spaces Defined by a Modulus Function

2010

The main purpose of this paper is to use the idea of n-norm and a modulus function to construct some multiplier sequence spaces with base space X, a real linear n-norm space. We study the spaces for linearity, existence of paranorm, completeness and some inclusion properties involving these spaces. Mathematics Subject Classification: 40A05, 46A45, 46E30

On Some I-Convergent Sequence Spaces Defined by a Modulus Function

2011

In this article we introduce the sequence spaces c I 0 (f), c I (f) and l I ∞ (f) for a modulus function f and study some of the properties of these spaces. Keywords: Ideal, filter,modulus function, Lipschitz function, I-convergence field, I-convergent, monotone and solid spaces. 2000 MSC: 40A05, 40A35, 40C05, 46A45.

Generalized vector-valued paranormed sequence space using modulus function

Applied Mathematics and Computation, 2010

In this paper we introduce a generalized vector-valued paranormed sequence space N p ðE k ; D m ; f ; sÞ using modulus function f, where p ¼ ðp k Þ is a bounded sequence of positive real numbers such that inf k p k > 0; ðE k ; q k Þ is a sequence of seminormed spaces with E kþ1 # E k for each k 2 N and s P 0. We have also studied sequence space N p ðE k ; D m ; f r ; sÞ, where f r ¼ f f f ;. .. ; f (r-times composition of f with itself) and r 2 N ¼ f1; 2; 3;. . .g. Results regarding completeness, K-space, normality, inclusion relations etc. are derived. Further, a study of multiplier of the set N p ðE k ; f ; sÞ is also made by choosing ðE k ; k Á k k Þ as sequence of normed algebras.

The χ2 sequence spaces defined by a modulus

2011

In this paper we introduce the following sequence spaces x ∈ χ 2 : P − lim k, ∞ m=0 ∞ n=0 a mn k f ((m + n)! |x mn |) 1 m+n = 0 and x ∈ Λ 2 : sup k, ∞ m=0 ∞ m=0 a mn k f |x mn | 1 m+n < ∞ where f is a modulus function and A is a nonnegative four dimensional matrix. We establish the inclusion theorems between these spaces and also general properties are discussed.