On some new paranormed euler sequence spaces and Euler Core

On compact operators and some EulerB(m)-difference sequence spaces

“…The Euler sequence spaces have been studied by several authors in [1,2] and [4][5][6][7][8][9]. Recently, the generalized difference matrix and the generalized difference matrix order m have been defined by Altay and Ba¸sar [10] and Ba¸sarır and Kayıkçı [3], respectively.…”

On paranormedλ-sequence spaces of non-absolute type

“…In the literature, the approach of constructing a new sequence space on the normed space or the paranormed space by means of the matrix domain of a particular limitation method has recently been employed by several authors; see, for example, Wang [2], Nq and Lee [3], Malkowsky and Savaş, [4] Malkowsky [5], Mursaleen and Noman [1] Altay and Başar [6,7], Altay et al [8], Başar and Altay [9][10][11], Aydın and Başar [12,13], Karakaya and Polat [14], Polat et al [15], Savaş et al [16] and Demiriz and Çakan [17]. Some of the above-mentioned authors introduced the following sequence spaces: [11], r t ∞ (p) = (ℓ ∞ (p)) R t , r t c (p) = (c(p)) R t and r t 0 (p) = (c 0 (p)) R t in [6], and e r 0 (∆; p) = (c 0 (p)) E r ∆ , e r (∆; p) = (c(p)) E r ∆ and e r ∞ (∆; p) = (ℓ ∞ (p)) E r ∆ in [14], where C 1 , R t , and E r denote the Cesâro, the Riesz, and the Euler means, respectively, ∆ denotes the band matrix of the difference operators, and Λ and G are defined in [1,4], respectively.…”

On the paranormed binomial sequence spaces

“…In [8], Demiriz and Ç akan have defined the sequence spaces e r 0 (u, p) and e r c (u, p) which consists of all sequences such that E r,u -transforms are in c 0 (p) and c(p), respectively E r,u = {e r nk (u)} is defined by…”

“…Also, we have constructed the basis and computed the α−, β − and γ−duals and investigated some topological properties of the spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p). Following Choudhary and Mishra [7], Başar and Altay [3], Altay and Başar [1,2], Demiriz [8], Kirişçi [14,15], Candan and Güneş [16] and Ellidokuzoglu and Demiriz [9], we define the sequence spaces b r,s 0 (p), b r,s c (p), b r,s ∞ (p) and b r,s (p), as the sets of all sequences such that B r,s −transforms of them are in the spaces c 0 (p), c(p), ∞ (p) and (p), respectively, that is, Define the sequence y = {y n (r, s)}, which will be frequently used, as the B r,s −transform of a sequence x = (x k ), i.e.,…”