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    On the Euler sequence spaces which include the spaces lp and l?I
    (Elsevier Science Inc, 2006) Altay, B; Basar, F; Mursaleen, M
    In the present paper, we introduce the Euler sequence space e(p)(r) consisting of all sequences whose Euler transforms of order r are in the space e,, of non-absolute type which is the BK-space including the space l(p) and prove that the spaces e(p)(r) and l(p) are linearly isomorphic for 1 <= p <= infinity. Furthermore, we give some inclusion relations concerning the space e(p)(r). Finally, we determine the alpha-, beta- and gamma-duals of the space e(p)(r) for 1 <= p <= infinity and construct the basis for the space e(p)(r), where 1 <= P <= infinity. (c) 2005 Elsevier Inc. All rights reserved.
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    On the fine spectrum of the difference operator ? on c0 and c
    (Elsevier Science Inc, 2004) Altay, B; Basar, F
    In the present paper, the fine spectrum of the difference operator on the sequence spaces c(0) and c have been examined and a Mercerian theorem has also been given. (C) 2004 Elsevier Inc. All rights reserved.
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    Some new difference sequence spaces
    (Elsevier Science Inc, 2004) Aydin, C; Basar, F
    The difference sequence spaces l(infinity)(Delta), c(Delta) and c(0)(Delta) were studied by Kizmaz [Canad. Math. Bull. 24 (2) (1981) 169]. The sequence spaces a(0)(r) and a(c)(r) have been recently defined and examined by Aydin and Basar in [Hokkaido Math. J., in press]. The main purpose of the present paper is to introduce the spaces a(0)(r)(Delta) and a(c)(r)(Delta) of difference sequences. Moreover, it is proved that the spaces a(0)(r)(Delta) and a(c)(r)(Delta) are the BK-spaces including the spaces c(0) and c, and some inclusion relations have been given. It is also proved that the sequence space a(0)(r) has AD property while the space a(0)(r)(Delta) has not. Furthermore, the basis and the alpha-, beta- and gamma-duals of the spaces a(0)(r)(Delta) and a(c)(r)(Delta) have been determined. The last section of the paper has been devoted to theorems on the characterizations of the matrix classes (a(c)(r)(Delta) : l(p)) and (a(c)(r)(Delta) : c), and the characterizations of some other matrix classes have been obtained by means of a given basic lemma, where 1 less than or equal to p less than or equal to infinity. (C) 2003 Elsevier Inc. All rights reserved.
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    Some new paranormed sequence spaces
    (Elsevier Science Inc, 2004) Aydin, C; Basar, F
    Maddox defined the sequence spaces l(infinity)(p), c(p) and c(0)(p) in [Proc. Camb. Philos. Soc. 64 (1968) 335, Quart. J. Math. Oxford (2) 18 (1967) 345]. In the present paper, the sequence spaces a(0)(r)(u,p) and a(c)(r)(u,p) of non-absolute type have been introduced and proved that the spaces a(0)(r)(u,p) and a(c)(r)(u,p) are linearly isomorphic to the spaces c(0)(p) and c(p), respectively. Besides this, the alpha-, beta- and gamma-duals of the spaces a(0)(r)(u,p) and a(c)(r)(u,p) have been computed and their basis have been constructed. Finally, a basic theorem has been given and later some matrix mappings from a(0)(r)(u,p) to the some sequence spaces of Maddox and to some new sequence spaces have been characterized. (C) 2003 Elsevier Inc. All rights reserved.
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    Some new spaces of double sequences
    (Academic Press Inc Elsevier Science, 2005) Altay, B; Basar, F
    In this study, we define the double sequence spaces BS, BS(t), CSp, CSbp, CSr and BV, and also examine some properties of those sequence spaces. Furthermore, we show that these sequence spaces are complete paranormed or normed spaces under some certain conditions. We determine the a-duals of the spaces BS, BV, CSbp and the alpha-duals of the spaces CSbp, and CSr of double series. Finally, we give the conditions which characterize the class of four-dimensional matrix mappings defined on the spaces CSbp, CSr and CSp of double series. (c) 2004 Elsevier Inc. All rights reserved.