On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C0, C, lP, (1 ≤ P ≤ ∞), W0 and W∞
Authors
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Universite du Havre ,FR
Bruno de Malafosse
DOI:
https://doi.org/10.18311/jims/2017/14852Keywords:
BK Space, Matrix Transformations, Multiplier of Sequence Spaces, Sequence Spaces Inclusion Equations, Sequence Spaces Inclusion Equations with OperatorAbstract
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 ∈ E; in particular, ca denotes the set of all sequences y such that y/a converges. Let Φ = {c0, c, l∞, lp, w0, w∞},(p≥1).. In this paper we apply a result stated in [9] and we deal with the class of (SSIE) of the form F ⊂ Ea+F'x where F∈{c0,lp, w0, w∞} and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (rn)n and we deal with the case when F = F'. Finally we solve the equation Er + (lp)x = lp with E = c0, c, s1, or lp (p≥1). These results extend those stated in [10].
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Copyright (c) 2017 Bruno de Malafosse
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2017-02-15
Published 2017-07-01
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