Rayees Ahmad and Syed Najamul Hasan, New Type of Generalized Difference Sequence Space, Volume 2017, Number 1, Pages 120-133, 2018

# Rayees Ahmad and Syed Najamul Hasan, New Type of Generalized Difference Sequence Space, Volume 2017, Number 1, Pages 120-133, 2018

Abstract: 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.

Keywords: Sequence space of non-absolute type; paranormed sequence space; K\"{o}the duals ; matrix transformations.