A Note on Some Strongly Sequence Spaces

A Note on Some Strongly Sequence Spaces

and Applied Analysis 3 P:4 p x y ≤ p x p y , for all x, y ∈ X triangle inequality , P:5 if λn is a sequence of scalars, with λn → λ n → ∞ , and xn is a sequence of vectors with p xn −x → 0 n → ∞ , then p λnxn −λx → 0 n → ∞ continuity of multiplication by scalars . A complete linear metric space is said to be a Fréchet space. A Fréchet sequence space X is said to be an FK space, if its metric is...

on strongly δn -summable sequence spaces

in the present paper we define strongly δn -summable sequences which generalize a-summablesequences and prove such spaces to be complete paranormed spaces under certain conditions, sometopological results have also been discussed.

A Note on Strongly Quotient Graphs

Calculations on some sequence spaces

where B = (bn)n≥1 is a one-column matrix and X the unknown, see [1, 2, 3, 4, 5, 6, 7, 8, 10]. Equation (1.2) can be written in the form AX = B, where AX = (An(X))n≥1. In this paper, we will also consider A an operator from a sequence space into another sequence space. A Banach space E of complex sequences with the norm ‖‖E is a BK space if each projection PnX = xn is continuous for all X ∈ E. A...

On Some Difference Sequence Spaces

In this article we define some difference sequence spaces using a new difference operator. We show that these spaces can be made BK-spaces under a suitable norm. We also find their isometrically isomorphic spaces and thus we find the dual of some of the spaces. Furthermore we study the spaces for separable space, reflexive space, Hilbert space and investigate for solid space, symmetric space, m...