4-Dimensional Euler-Totient Matrix Operator and Some Double Sequence Spaces
Abstract
Our main purpose in this study is to define
the 4-dimensional Euler-Totient matrix operator and to investigate the matrix domains
of this matrix on the classical double sequence spaces $\mathcal{M}_{u}$, $\mathcal{C}_{p}$, $\mathcal{C}_{bp}$ and $\mathcal{C}_{r}$.
Besides these, we examine their topological and algebraic properties and give inclusion relations about the new spaces.
Also, the $\alpha-$, $\beta(\vartheta)-$ and $\gamma-$duals of these spaces are determined and finally, some matrix classes are characterized.
Keywords
Euler function,Möbius function,4-dimensional Euler-Totient matrix operator,Double sequence spaces
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