λ-Core of a Sequence and Related Inequalities

The sequence spaces c sup λ /sup and cs sup λ /sup have recently been introduced in and, respectively, as the sets of all sequences whose Λ- transforms are in the spaces c and cs, respectively. The main purpose of this study is to introduce the new type cores, Κ sub Λ /sub - core and S sub Λ /sub -- core, of a real valued sequence and also determine necessary and sufficient conditions for a matrix Λ to satisfy Κ sub Λ /sub - core(Ax) ⊆ Κ -- core(x), Κ sub Λ /sub - core (Ax) ⊆ σ - core (x), Κ sub Λ /sub - core(Ax) ⊆ st - core(x), and S sub Λ /sub = core(x), for all x l sub ∞ /sub .