Subordinations of the solutions of Briot-Bouquet differential equations and their applications

In this paper, we give some sufficient and necessary conditions for subordination of the solution of the Briot-Bouquet differential equation: p(z) + zp'(z)/delta p(z)+lambda = g(z), p(0) = g(0) = 1, z is an element of U, where delta and lambda are real numbers with delta not equal 0, delta + lambda > 0, and U is the unit disc in the complex plane C. Using these subordinations, we obtain some sufficient and necessary conditions that the integral operators [GRAPHICS] preserve starlikeness, where alpha, beta, delta, and gamma are real numbers with alpha + delta = beta + gamma > 0, alpha beta not equal 0.