Simple Norm Inequalities.

The article discusses theorems on triangle inequality and reverse inequality on normed spaces. Theorem 1 states that for nonzero vectors, given values for x and y, in a normed space the result would result into an inequality. If x = y = 1 then there is an equality. A generalization can be proven through a Massera-Schaffer inequality. A second theorem for triangle inequality and the corresponding proof is also provided which demonstrates the strengthening of the triangle inequality and its reverse inequality in normed spaces.