International Journal of Advances in Mathematics
International Journal of Advances in Mathematics
2456-6098
Volume 2018
Number 1
2018
January
1
New Type of Generalized Difference Sequence Space
120
133
EN
Rayees
Ahmad
School of Sciences, Maulana Azad National Urdu University,
Gachibowli, Hyderabad,
India.
rayeesmanuu@rediffmail.com
Syed Najamul
Hasan
School of Sciences, Maulana Azad National Urdu University,
Gachibowli, Hyderabad,
India.
rayeesmanuu@rediffmail.com
The space $r^q(u,p,s)$ of non-absolute type have recently been introduced and studied (see, M. F. Rahman and A. B. M. R. Karim, Generalized Riesz sequence space of non-absolute type and some matrix mappings, Pure and Applied Math. Journal, 4(3)(2015), 90-95). In the present paper, we introduce the space $r^{q}( \triangle^{p}_{u}(s))$, we show its completeness property , prove that the space $r^{q}( \triangle^{p}_{u}(s))$ and $l(p)$ are linearly isomorphic and compute their K\"{o}the-duals. Furthermore, we construct its basis and in our last section, we have characterized some matrix classes of infinite matrices.
Sequence space of non-absolute type; paranormed sequence
space; K\"{o}the duals ; matrix transformations.
http://adv-math.com/rayees-ahmad-syed-najamul-hasan-new-type-generalized-difference-sequence-space-volume-2017-number-1-pages-120-133-2018/
http://adv-math.com/wp-content/uploads/2018/01/RayeesRDS-1.pdf