New Paranormed Sequence Spaces l∞(p,λ) , c(p,λ) and c0(p,λ) Generated by an Infinite Matrix (original) (raw)

On some new paranormed sequence spaces defined by the matrix (D )(r,0,0,s)

Proyecciones (antofagasta), 2021

In this paper, we introduce some new paranormed sequence spaces and study some topological properties. Further, we determine α, β and γ-duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of matrix mappings.

On some properties of new paranormed sequence space of non-absolute type

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.

New Type of Sequence Spaces of Non-Absolute Type and Some Matrix Transformations

2014

In this paper, we introduce the sequence space eu(p). We show it posses BK-property, prove that the space eu(p) and l(p) are linearly isomorphic to each other and also compute the α-, βand γ-duals of eu(p) and discuss some of its inclusion properties. Furthermore, we construct the basis of eu(p). Moreover, we characterize the classes (e r u(p) : lp) and (eu(p) : f) of infinite matrices. 1. Preliminaries, Background and Notation Let ω denote the space of all sequences(real or complex). The family under pointwise addition and scalar multiplication forms a linear(vector)space over real of complex numbers. Any subspace of ω is called the sequence space. So the sequence space is the set of scalar sequences(real of complex) which is closed under co-ordinate wise addition and scalar multiplication. Throughout the paper N, R and C denotes the set of non-negative integers, the set of real numbers and the set of complex numbers, respectively. Let l∞, c and c0, respectively, denotes the space ...