Let f : ${mathbb{R}}{ ightarrow}{mathbb{C}}$. We consider the Hyers-Ulam stability of Jensen type functional inequality $$|f(px+qy)-Pf(x)-Qf(y)|{leq}{epsilon}$$ in the half planes {(x, y) : $kx+sy{geq}d$} for fixed d, k, $s{in}{mathbb{R}}$ with $k{ eq}0$ or $s{ eq}0$. As consequences of the results we obtain the asymptotic behaviors of f satisfying $$|f(px+qy)-Pf(x)-Qf(y)|{ ightarrow}0$$ as $kx+sy{ ightarrow}{infty}$.