There are many classes of analytic and $p$-valent functions
in the unit disk U.N.S. Sohi studied a class $S_p(\alpha)$ of analytic
and $p$-valent functions
$$
f(z)= z^p+ \sum_{n=1}^\infty a_{p+n}z^{p+n},\qquad (p\in N)
$$
in the unit disk $U$ satisfying the condition
$$
|f'(z)/pz^{p-1}-\alpha|<\alpha,\qquad (z\in U)
$$
for $\alpha >1/2$. In this paper, we consider a new subclass
$S_{p,k}(\alpha)$ of analytic and $p$-valent functions
$$
f(z)= z^p+\sum a_{p+n}z^{p+n},\qquad (p\in N)
$$
in the unit disk $U$ satisfying the condition
$$
łeft|\frac{\Gamma(p+1-k)D^k_z(z)}{\Gamma(p+1)z^{p-k}}\right|<\alpha,
\qquad (z\in U)
$$
for $0