A New Difference Sequence Set of Order α and Its Geometrical Properties

Abstract

We introduce a new class of sequences named as $m_{\alpha }\left({\mathrm{\Delta }}^r,\varphi ,p\right)$ and, for this space, we study some inclusion relations, topological properties, and geometrical properties such as order continuous, the Fatou property, and the Banach-Saks property of type $p$.