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The aim of this paper is to introduce the normed binomial sequence spaces    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$b^{r,s}_{p}(\nabla)$\end{document}    b  p   r  ,  s    (  ∇  )by combining the binomial transformation and difference operator, where    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$1\leq p\leq\infty$\end{document}   1  ≤  p  ≤  ∞. We prove that these spaces are linearly isomorphic to the spaces    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$\ell_{p}$\end{document}    ℓ  pand    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$\ell _{\infty}$\end{document}    ℓ  ∞, respectively. Furthermore, we compute Schauder bases and the  α -,  β - and  γ -duals of these sequence spaces.

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