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].

Some Vector FK Sequence Spaces Generated by Modulus Function

Journal of Research in Mathematics Trends and Technology, 2020

In this paper, some vector valued sequence spaces and using modulus function are presented. Furthermore, we examined some topological properties of these sequence spaces equipped with a paranorm.

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.