The binomial sequence spaces of nonabsolute type

Abstract

In this paper, we introduce the binomial sequence spaces b

On some binomial B ( m ) $B^{(m)}$ -difference sequence spaces

“…The sequence spaces , and are BK -spaces with their sup-norm (see [24], Theorem 2.1 and [25], Theorem 2.1). Moreover, is a triangle matrix and (2.1) holds.…”

“…Recently Bişgin [24, 25] defined another generalization of the Euler sequence spaces and introduced the binomial sequence spaces , , and . Let and .…”

“…These new sequence spaces are the generalization of the sequence spaces defined in [24, 25] and [23]. Also, we give some inclusion relations and compute the bases and α -, β - and γ -duals of these sequence spaces.…”

On the paranormed binomial sequence spaces

“…for all k, n ∈ N and 0 < r < 1. In [5] and [6], the Binomial sequence spaces b r,s 0 , b r,s c , b r,s ∞ and b r,s p , which are the matrix domains of Binomial mean B r,s in the sequence spaces c 0 , c, ∞ and p , respectively, are introduced, some inclusion relations and Schauder basis for the spaces b r,s 0 , b r,s c , b r,s ∞ and b r,s p are given, and the α−, β − and γ− duals of those spaces are determined. For more papers related to sequence spaces and matrix domains of different infinite matrices one can see [13,12] and references therein.…”

Some normed binomial difference sequence spaces related to the ℓ p $\ell_{p}$ spaces

“…Recently Bişgin [19, 20] defined another type of generalization of the Euler sequence spaces and introduced the binomial sequence spaces , , and . Let and .…”