On the euler sequence spaces which include the spaces łp and ł∞ II

By , we mean the space of all sequences whose Euler transforms of order r are in the sequence spaces lp and l{infinity} (see [B. Altay, F. Basar, M. Mursaleen, On the Euler sequence spaces which include the spaces lp and l{infinity} I, Inform. Sci. (2005) (in press)]), where 1 < =p < {infinity}. In the present paper, we essentially characterize the classes and of infinite matrices for 1 < p < ={infinity} and give the characterizations of some other matrix mappings from the space to the Euler, Riesz, difference, etc., sequence spaces, by means of a given basic lemma. We devote the final section of the paper to examining some geometric properties of the space .