Finite Field Tarski-Maligranda Inequalities

Let F be a sub-modulus field such that 2̸ = 0. Let X be a sub-normed linear space over F. Then we show that ∥x∥ − ∥y∥ ≤ 2 |2| ∥x + y∥ + 2 |2| max{∥x − y∥, ∥y − x∥} − (∥x∥ + ∥y∥) and ∥x∥ − ∥y∥ ≤ ∥x∥ + ∥y∥ − 2 |2| ∥x + y∥ + 2 |2| max{∥y − x∥, ∥x − y∥}. Above inequalities are finite field versions of important Tarski-Maligranda inequalities obained by Maligranda [Banach J. Math. Anal., 2008].