On sequence spaces equations of the form ET + Fx = Fb for some triangle T
Author
Source
Jordan Journal of Mathematics and Statistics
Issue
Vol. 8, Issue 1 (31 Mar. 2015), pp.79-105, 27 p.
Publisher
Yarmouk University Deanship of Research and Graduate Studies
Publication Date
2015-03-31
Country of Publication
Jordan
No. of Pages
27
Main Subjects
Abstract EN
Given any sequence a = (an) n ≥ 1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn) n ≥ 1 such that y / a = (yn / an) n ≥ 1 2 E ; in particular, sa(c) denotes the set of all sequences y such that y / a converges.
We denote by w ∞ and w 0 the sets of all sequences y such that supn (n-1 Σ n k = 1 |yk|) =0.
We also use the sets of analytic and entire sequences denoted by ⋀ and Γ and defined by supn |yn| 1 / n < ∞ and limn →∞ |yn|1 / n = 0, respectively.
In this paper we explicitly calculate the solutions of (SSE) of the form ET + Fx = Fb in each of the cases E = c, l ∞, l p (p ≥ 1), wo, Γ or Λ, F = c, or l∞, and T is either of the triangles ∆, or Σ, where ∆ is the operator of the first difference, and Σ is the operator defined by Σ ny = Σ n k = 1 yk.
For instance the solvability of the (SSE) Γ Σ + Λ I = Λ b consists in determining the set of all positive sequences I = (In)n that satisfy the statement : supn {(|yn| / b n) 1 / n} < ∞ if and only if there are u, v ∈ ω with y = u + v such that n lim n → ∞ |Σ uk| k = 11 / n = 0 and sup { (|vn| / In) 1 / n} < ∞ for all y.
American Psychological Association (APA)
Malafosse, Bruno De. 2015. On sequence spaces equations of the form ET + Fx = Fb for some triangle T. Jordan Journal of Mathematics and Statistics،Vol. 8, no. 1, pp.79-105.
https://search.emarefa.net/detail/BIM-565967
Modern Language Association (MLA)
Malafosse, Bruno De. On sequence spaces equations of the form ET + Fx = Fb for some triangle T. Jordan Journal of Mathematics and Statistics Vol. 8, no. 1 (Mar. 2015), pp.79-105.
https://search.emarefa.net/detail/BIM-565967
American Medical Association (AMA)
Malafosse, Bruno De. On sequence spaces equations of the form ET + Fx = Fb for some triangle T. Jordan Journal of Mathematics and Statistics. 2015. Vol. 8, no. 1, pp.79-105.
https://search.emarefa.net/detail/BIM-565967
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 104-105
Record ID
BIM-565967