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The aim of this paper is to introduce the normed binomial sequence spaces bpr,s(∇)$b^{r,s}_{p}(\nabla)$ by combining the binomial transformation and difference operator, where 1≤p≤∞$1\leq p\leq\infty$. We prove that these spaces… Click to show full abstract
The aim of this paper is to introduce the normed binomial sequence spaces bpr,s(∇)$b^{r,s}_{p}(\nabla)$ by combining the binomial transformation and difference operator, where 1≤p≤∞$1\leq p\leq\infty$. We prove that these spaces are linearly isomorphic to the spaces ℓp$\ell_{p}$ and ℓ∞$\ell _{\infty}$, respectively. Furthermore, we compute Schauder bases and the α-, β- and γ-duals of these sequence spaces.
Keywords:
binomial difference;
sequence spaces;
difference sequence;
normed binomial;
sequence
Journal Title: Journal of Inequalities and Applications
Year Published: 2017
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Journal Title: Journal of Inequalities and Applications
Year Published: 2017
Link to full text (if available)
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recommendations!