On the spaces of Euler almost null and Euler almost convergent sequences

Let Er denotes the Euler means of order r. The Euler sequence spaces e0, e r c and e r p, e r ∞ consisting of all sequences whose E r-transforms are in the spaces c0, c and `p, `∞ are introduced by Altay and Başar [2], Altay et al. [3], and Mursaleen et al. [22]. Recently, Polat and Başar have studied the Euler spaces of difference sequences of order m, in [24]. The concept almost convergence of a bounded sequence introduced by Lorentz [19]. Quite recently, Başar and Kirişci have worked the domain of the generalized difference matrix B(r, s) in the sequence spaces f0 and f of almost null and almost convergent sequences, in [8]. In this paper, following Başar and Kirişci [8], we essentially deal with the domains (f0)Er and fEr of the Euler means of order r in the spaces f0 and f . Therefore, we add two new spaces to the Euler sequence spaces.