Mr-factors and Qr-factors for near quasinorm on certain sequence spaces

such that (i) |0| = 0, (ii) |x| ≥ 0, for all x ∈ X , (iii) |− x| = |x|, for all x ∈ X , (iv) |x+ y| ≤ |x|+ |y|, for all x, y ∈ X , (v) if tk ∈ F, |tk − t| → 0, and xk, x ∈ X , |xk − x| → 0, then |tkxk − tx| → 0. If | · | satisfies only properties (i) to (iv), then we call | · | a near quasinorm. If the quasinorm satisfies |x| = 0 if and only if x = 0, then it is said to be total. A quasinormed linear space (QNLS) is a pair (X ,| · |) where | · | is a quasinorm on X . If (X ,| · |) is a quasinorm space, then the map | · | : X → R is continuous. For p > 0, a p-seminorm on X is a function ‖ · ‖ : X → R satisfying (i) ‖x‖ ≥ 0, for all x ∈ X , (ii) ‖tx‖ = |t|p‖x‖, for all t ∈ F, for all x ∈ X , (iii) ‖x+ y‖ ≤ ‖x‖+‖y‖, for all x, y ∈ X .