ID | 52077 |
フルテキストURL | |
著者 |
Malafosse, Bruno de
LMAH Université du Havre
Malkowsky, Eberhard
Fatih University
|
抄録 | Given any sequence z = (zn)n≥1 of positive real numbers
and any set E of complex sequences, we write Ez for the set of all
sequences y = (yn)n≥1 such that y/z = (yn/zn)n≥1 ∈ E; in particular,
sz(c)
denotes the set of all sequences y such that y/z converges. In this
paper we deal with sequence spaces inclusion equations (SSIE), which
are determined by an inclusion each term of which is a sum or a sum
of products of sets of sequences of the form Xa(T) and Xx(T) where
a is a given sequence, the sequence x is the unknown, T is a given
triangle, and Xa(T) and Xx(T) are the matrix domains of T in the set X
. Here we determine the set of all positive sequences x for which the
(SSIE) sx(c)
(B(r, s)) sx(c)⊂
(B(r', s')) holds, where r, r', s' and s are real
numbers, and B(r, s) is the generalized operator of the first difference
defined by (B(r, s)y)n = ryn+syn−1 for all n ≥ 2 and (B(r, s)y)1 = ry1.
We also determine the set of all positive sequences x for which
ryn + syn−1 /xn
→ l implies
r'yn + s'yn−1
/xn
→ l (n → ∞) for all y
and for some scalar l. Finally, for a given sequence a, we consider the
a–Tauberian problem which consists of determining the set of all x such
that sx(c) (B(r, s)) ⊂ sa(c) .
|
キーワード | Matrix transformations
BK space
the spaces s<sub>a</sub>, s<doubleint><sub>a</sub><sup>0</sup></doubleint> and s<sub>a</sub><sup>(c)</sup>
(SSIE)
(SSE) with operator
band matrix B(r, s)
Tauberian result
|
発行日 | 2014-01
|
出版物タイトル |
Mathematical Journal of Okayama University
|
巻 | 56巻
|
号 | 1号
|
出版者 | Department of Mathematics, Faculty of Science, Okayama University
|
開始ページ | 179
|
終了ページ | 198
|
ISSN | 0030-1566
|
NCID | AA00723502
|
資料タイプ |
学術雑誌論文
|
言語 |
英語
|
著作権者 | Copyright©2014 by the Editorial Board of Mathematical Journal of Okayama University
|
論文のバージョン | publisher
|
査読 |
有り
|
Submission Path | mjou/vol56/iss1/14
|
JaLCDOI |