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

Given any sequence a = (a_n)_n≥1 of positive real numbers and any set E of complex sequences, we write E_a for the set of all sequences y = (y_n)_n≥1 such that y/a = (y_n/a_n)_n≥1 ∈ E; in particular, c_a denotes the set of all sequences y such that y/a converges. Let Φ = {c₀, c, l_∞, l_p, 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 ⊂ E_a+F'_x where F∈{c_0,l_p, 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 E_r + (l_p)_x = l_p with E = c₀, c, s₁, or l_p (p≥1). These results extend those stated in [10].