Two Parameter Families of Close-to-Convex Functions and Convolution Theorems

Abstract

Using a recently obtained coefficient condition for functions with positive real part by M. Obradovic and S. Ponnusamy, we construct four different useful examples of two parameter families of close-to-convex functions. As a consequence of another well-known coefficient condition due to M. Obradovic and S. Ponnusamy, we obtain a number of results concerning the convolution of two univalent functions. Using these results, we obtain criteria for combinations of hypergeometric functions to be univalent.