Pri 26D15, 47A30; Sec 46A45.

In this work, we give a generalization of Hölder and Minkowski inequalities to normal sequence algebras with absolutely monotone seminorm. Our main result is Theorem 2.1 and Theorem 2.2 which state these extensions. Taking and in both these theorems, we obtain classical versions of these inequalities. Also, using these generalizations we construct the vector-valued sequence space as a paranormed space which is a most general form of the space investigated in [6].