Some new paranormed sequence spaces

On Some Euler Sequence Spaces of Nonabsolute Type

“…Quite recently, Aydın and Başar have studied the sequence spaces c A r [7], and a r 0 ( ) [8] and extended the sequence spaces a r 0 and a c r to the paranormed spaces a p r 0 ( ) and a p c r ( ) in [9]; here, A r denotes the matrix A r = a nk for all k, n ∈ N and any fixed r ∈ R. In the present paper, following [2 -9], we introduce Euler sequence spaces e r 0 and e c r of nonabsolute type and obtain some results related to these sequence spaces. Furthermore, …”

On the Euler sequence spaces which include the spaces ℓp and ℓ∞ I☆

“…The approach constructing a new sequence space by means of the matrix domain of a particular limitation method has recently been employed by Wang [16], Ng and Lee [13], Malkowsky [11], Bas ßar and Altay [6], Altay and Bas ßar [2], Malkowsky and Savas ß [12] and Aydın and Bas ßar [3][4][5]. They introduced the sequence spaces ð' 1 Þ N q and c N q in [16]…”

Survey on the domain of the matrix lambda in the normed and paranormed sequence spaces

“…If A is triangle, then one can easily observe that the sequence spaces X A and X are linearly isomorphic, i.e., X A = X. The idea constructing a new sequence space by means of the domain of a triangle matrix was employed by Wang [48], Ng and Lee [43], Malkowsky [29], Altay and Başar [1,2,3,4,5,6,7,8], Malkowsky and Savaş [33], Başar¬r [17,18], Başar¬r and Kay¬kç¬ [19], Başar¬r and Öztürk [20], Kara and Başar¬r [21], Kara et al [22], Ayd¬n and Başar [9,10,11,12,13], Başar et al [16],Şengönül and Başar [47], Altay [1], Polat and Başar [44] and, Malkowsky et al [30]. Additionally, c 0 (u; p) and c(u; p) are the spaces consisting of the sequences x = (x k ) such that ux = (u k x k ) is in the spaces c 0 (p) and c(p) for u 2 U, the set of sequences with non-zero entries, respectively, and studied by Başar¬r [17].…”