Let H be a separable complex H be a space and let (equation omitted)(H) be the *-algebra of all bounded linear operators on H. An operator T in (equation omitted)(H) is said to be p-hyponormal if ($T^{ast}T)^p - (TT^{ast})^{p}geq$ 0 for 0 ＜ p ＜ 1. If p = 1, T is hyponormal and if p = $frac{1}{2}$, T is semi-hyponormal. In this paper, by using a technique introduced by S. K. Berberian, we show that the approximate point spectrum <TEX>$sigma_{alpha p}(T) of a pure p-hyponormal operator T is empty, and obtains the compact perturbation of T.