On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C 0 , C, l P , (1 ≤ P ≤ ∞), W 0 and W ∞

Abstract

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 = {c 0 , c, l ∞ , l p , w 0 , 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 , w 0 , w ∞ } and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (r n ) n and we deal with the case when F = F'. Finally we solve the equation E r + (l p ) x = l p with E = c 0 , c, s 1 , or l p (p≥1). These results extend those stated in [10].