The binomial sequence spaces which include the spaces ℓ p $\ell_{p}$ and ℓ ∞ $\ell_{\infty}$ and geometric properties

Abstract

Abstract

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

“…These spaces are the natural continuations of [1, 7, 20]. Our results are the generalizations of the matrix domain of the Euler matrix of order r .…”

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

“…So the binomial matrix generalizes the Euler matrix. Bişgin [20] defined the following spaces of binomial sequences: and …”

“…These new sequence spaces are the generalization of the sequence spaces defined in [7] and [20]. Also, we compute the bases and α -, β - and γ -duals of these sequence spaces.…”

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

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