Euler-Riesz Difference Sequence Spaces

Authors : Hacer BİLGİN ELLİDOKUZOĞLU, Serkan DEMİRİZ

Pages : 63-72

View : 22 | Download : 10

Publication Date : 2017-12-19

Article Type : Research Paper

Abstract :Ba\c{s}ar and Braha \cite{braha-basar-2016}, introduced the sequence spaces $\ell_\infty$, $c$ and $c_0$  of Euler- Ces\`{a}ro bounded, convergent and null difference sequences and studied their some properties. The main purpose of this study is to introduce the sequence spaces ${[\ell_\infty]}_{e.r},{[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler- Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$  with backward difference operator $\Delta$. Furthermore, the inclusions $\ell_\infty\subset{[\ell_\infty]}_{e.r}, c\subset {[c]}_{e.r}$ and $c_0\subset{[c_0]}_{e.r}$ strictly hold, the basis of the sequence spaces ${[c_0 ]}_insert ignore into journalissuearticles values(e.r);$ and ${[c]}_insert ignore into journalissuearticles values(e.r);$ is constucted and alpha-, beta- and gamma-duals of these spaces are determined. Finally, the classes of matrix transformations from the Euler- Riesz difference sequence spaces to the spaces $\ell_\infty, c$ and $c_0$ are characterized. 
Keywords : Euler sequence spaces, Riesz sequence spaces, matrix transformations