Paranorm I-convergent sequence spaces

2012

In this paper we present new classes of sequence spaces using the concept of n-norm and to investigate these spaces for some linear topological structures as well as examine these spaces with respect to derived (n-1) norms. We use an Orlicz function, a bounded sequence of positive real numbers and m operator to construct these spaces so that they became more generalized. This investigations will enhance the acceptability of the notion of n-norm by giving a way to contruct dierent sequence spaces with elements in n-normed space.

Journal of Mathematics, 2013

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.

2011

In this work, we introduce some new generalized sequence space related to the space l(p). Furthermore we investigate some topological properties as the completeness, the isomorphism and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute alpha-, beta- and gamma-duals of this space, and characterize certain matrix transformations on this sequence space.

2014

The aim of this paper is to introduce and study a new class c0 ((Smn , || . ||mn),  – , u – ) of double sequences with their terms in a normed space S as a generalization of the familiar sequence space c0 . We investigate the condition in terms of  – and u – so that a class is contained in or equal to another class of same kind and thereby derive the conditions of their equality. We further explore some of the preliminary results that characterize the linear topological structures of the space c0 ((Smn , || . ||mn),  – , u – ) when topologized it with suitable natural paranorm .

Afrika Matematika, 2014

In this article we introduce and study paranorm I-convergent sequence spaces S I (p), S I 0 (p) and S I ∞ (p) with the help of compact operator T on the real space R and a bounded sequence p = (p k) of positive real numbers. We study some topological and algebraic properties, prove the decomposition theorem and study some inclusion relations on these spaces. Keywords Compact operator • Ideal • Filter • I-convergent sequence • Solid and monotone space • Banach space • Paranorm Mathematics Subject Classification 41A10 • 41A25 • 41A36 • 40A30 1 Introduction and preliminaries Let N, R and C be the sets of all natural, real and complex numbers, respectively. We denote the space of all real or complex sequences by ω = {x = (x k) : x k ∈ R or C}. Let ∞ , c and c 0 be denote the Banach spaces of bounded, convergent and null sequences of reals, respectively with norm

Mathematical and Computer Modelling, 2011

Paranormed sequence space α-, β-, and γ -duals Weighted mean λ-sequence spaces Matrix mapping a b s t r a c t

Journal of Advanced College of Engineering and Management, 2016

The aim of this paper is to study some of the basic scalar and vector valued sequence spaces .We also study the topological structures of some of the basic sequence spaces when topologized through a norm or a paranorm.

Applied Mathematics and Computation, 2004

The idea of difference sequence spaces was introduced by Kızmaz [Canad. Math. Bull. 24 (1981) 169] and this concept was generalized by Et and C ß olak [Soochow J. Math. 21 (1995) 337]. In this paper we define the sequence spaces ' 1 ðpÞðD r v Þ, cðpÞðD r v Þ, c 0 ðpÞðD r v Þ and cðpÞðD r v Þ, ðr 2 NÞ, give some topological properties and inclusion relations of these sequence spaces.

Abstract In this paper we introduce, using a modulus function, some multiplier difference sequence spaces with base space X, a real linear n-normed space. We investigate the spaces for several algebraic and topological properties relevant to thus constructed spaces. Further we investigate the spaces for solidity, monotonicity, symmetricity and convergence free. Keywords: n-norm, difference sequence, modulus function, paranorm, completeness, solidity, symmetricity, convergence free, monotone space.

BIBECHANA, 2013

In this paper we introduce and study a new class c0 ( S, α‾ , u‾ , ||. , .|| ) of sequences with values in 2- normed space as a generalization of basic null sequence space c0. We investigate some conditions pertaining to the containment relations of the class c0 ( S, α‾ , u‾ , ||. , .|| ) in terms of different α‾ and u‾ and explore the linear topological structures of the space c0 ( S, αoline; , u‾ , ||. , .|| ) by endowing it with a suitable natural paranorm. BIBECHANA 10 (2014) 20-30 DOI: http://dx.doi.org/10.3126/bibechana.v10i0.9308