On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C0, C, lP, (1 ≤ P ≤ ∞), W0 and W∞
<p>Given any sequence a = (a<sub>n</sub>)<sub>n≥1</sub> of positive real numbers and any set <em>E</em> of complex sequences, we write E<sub>a</sub> for the set of all sequences y = (y<sub>n</sub>)<sub>n≥1</sub> such that y/a = (y<sub>n</sub>/a<sub>n</sub>)<sub>n≥1</sub> ∈ E; in particular, c<sub>a</sub> denotes the set of all sequences y such that y/a converges. Let Φ = {c<sub>0</sub>, c, l<sub>∞</sub>, l<sub>p</sub>, w<sub>0</sub>, w<sub>∞</sub>},(p≥1).. In this paper we apply a result stated in [9] and we deal with the class of (SSIE) of the form F ⊂ E<sub>a</sub>+F'<sub>x</sub> where F∈{c<sub>0,</sub>l<sub>p</sub>, w<sub>0</sub>, w<sub>∞</sub>} and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (r<sup>n</sup>)<sub>n</sub> and we deal with the case when F = F'. Finally we solve the equation E<sub>r</sub> + (l<sub>p</sub>)<sub>x</sub> = l<sub>p</sub> with E = c<sub>0</sub>, c, s<sub>1</sub>, or l<sub>p</sub> (p≥1). These results extend those stated in [10].</p>