TY  - JOUR
TT  - Euler-Riesz Difference Sequence Spaces
AU  - Bilgin Ellidokuzoğlu, Hacer
AU  - Demiriz, Serkan
PY  - 2017
DA  - December
JF  - Turkish Journal of Mathematics and Computer Science
JO  - TJMCS
PB  - Matematikçiler Derneği
WT  - DergiPark
SN  - 2148-1830
SP  - 63
EP  - 72
VL  - 7
KW  - Euler sequence spaces
KW  - Riesz sequence spaces
KW  - matrix transformations
N2  - Ba\c{s}ar and Braha \cite{braha-basar-2016}, introduced thesequence spaces $\ell_\infty$, $c$ and $c_0$ of Euler- Ces\'{a}robounded, convergent and null difference sequences and studiedtheir some properties. The main purpose of this study is tointroduce the sequence spaces ${[\ell_\infty]}_{e.r},{[c]}_{e.r}$and ${[c_0]}_{e.r}$ of Euler- Riesz bounded, convergent and nulldifference 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 thesequence spaces ${[c_0 ]}_(e.r)$ and ${[c]}_(e.r)$ is constuctedand 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.
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UR  - https://dergipark.org.tr/en/pub/tjmcs/issue//334615
L1  - https://dergipark.org.tr/en/download/article-file/386483
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