Difference Sequence Spaces Derived by using Pascal Transform

Authors : Saadettin AYDIN, Harun POLAT

Pages : 56-62

Doi:10.33401/fujma.541721

View : 16 | Download : 10

Publication Date : 2019-06-17

Article Type : Research Paper

Abstract :The essential goal of this manuscript is to investigate some novel sequence spaces of $p_{\infty }\leftinsert ignore into journalissuearticles values( \Delta \right); $, $p_{c}\leftinsert ignore into journalissuearticles values( \Delta \right); $ and $p_{0}\leftinsert ignore into journalissuearticles values( \Delta \right); $ which are comprised by all sequence spaces whose differences are in Pascal sequence spaces $p_{\infty }$, $p_{c}$ and $p_{0}$, respectively. Furthermore, we determine both $\gamma $-, $\beta $-, $\alpha $- duals of newly defined difference sequence spaces of $p_{\infty }\leftinsert ignore into journalissuearticles values( \Delta \right); $, $% p_{c}\leftinsert ignore into journalissuearticles values( \Delta \right); $ and $p_{0}\leftinsert ignore into journalissuearticles values( \Delta \right); $. We also obtain bases of the newly defined difference sequence spaces of $p_{c}\leftinsert ignore into journalissuearticles values( \Delta \right); $ and $p_{0}\leftinsert ignore into journalissuearticles values( \Delta \right); $. Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes $insert ignore into journalissuearticles values(p_{c}\leftinsert ignore into journalissuearticles values( \Delta \right); :l_{\infty });$ and $insert ignore into journalissuearticles values(p_{c}\leftinsert ignore into journalissuearticles values( \Delta \right); :c);$ are characterized.
Keywords : Pascal difference sequence spaces, Difference operator, matrix mappings, Pascal difference sequence spaces