ON THE SPACES OF EULER ALMOST NULL AND EULER ALMOST CONVERGENT SEQUENCES

Abstract

Let Er denotes the Euler means of order r. The Euler sequence spaces er 0,er c and er p,er 1 consisting of all sequences whose Er-transforms are inthespacesc0,cand`p,`1areintroducedby Altay andBasar [2],Altayet al. [3],and Mursaleen et al. [22]. Recently,Polat and Basar have studied the Euler spacesofdi§erence sequencesoforder m,in [24]. The concept almost convergence of a bounded sequence introduced by Lorentz [19]. Quite recently, Ba?sar and Kiri?sci have worked the domain of the generalized di§erence matrix B(r;s) in the sequence spaces f0 and f of almost null and almost convergent sequences,in [8]. In this paper,following Basar and Kirisci [8],weessentially dealwiththe domains (f0)Er and fEr of theEulermeansoforderrinthespacesf0 and f. Therefore,weaddtwonew spacesto the Euler sequence spaces.