Starlikeness and close-to-convexity involving certain differential inequalities

In the present paper, we study certain differential inequalities involving meromorphic functions in the open unit disk and obtain certain sufficient conditions for starlikeness and close -to -convexity of meromorphic functions. In particular, we obtain: 1. If f(z) E sigma p satisfies the differential inequality | 1 +zf ''(z)f '(z)+p divided by divided by divided by divided by<12, z is an element of E, | then f(z) is meromorphic close -to -convex function. 2. If f(z) E sigma satisfies the differential inequality |zf '(z)/f(z)+ 1 divided by(1-gamma )divided by 1 +zf ''(z)/f '(z)-zf '(z)f(z)divided by divided by divided by divided by gamma<1-alpha(1 +|1-2 alpha|)gamma, gamma >= 0, z is an element of E, then f(z) is meromorphic starlike function of order alpha.