On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C0, C, lP, (1 ≤ P ≤ ∞), W0 and W

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Authors

  • Universite du Havre ,FR

DOI:

https://doi.org/10.18311/jims/2017/14852

Keywords:

BK Space, Matrix Transformations, Multiplier of Sequence Spaces, Sequence Spaces Inclusion Equations, Sequence Spaces Inclusion Equations with Operator

Abstract

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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Published

2017-07-01

How to Cite

Malafosse, B. de. (2017). On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C<sub>0</sub>, C, l<sub>P</sub>, (1 &#8804; P &#8804; &#8734), W<sub>0</sub> and W<sub>&#8734</sub>. The Journal of the Indian Mathematical Society, 84(3-4), 211–224. https://doi.org/10.18311/jims/2017/14852
Received 2017-02-03
Accepted 2017-02-15
Published 2017-07-01

 

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