On the Derivatives of Integral Functions

The object of this paper is to investigate some inequalities concerning integral functions. Let f(z) be an integral function of order P and lower order λ and let f^(s)(z) be the sth derivative of f(z) and let M^(r) M ⁽¹⁾(r),… denote the maximum moduli of f(z), f⁽¹⁾(z)>"- respectively, on the circle \z\ = r. Let n(r, f) = n(r) denote, as usual, the number of zeros of f(z) lying in the circle |z| = r and on its circumference and let m(r) = min \f(z)\.