Abstract

We consider functions f analytic in the unit disc and assume the power series representation of the form f(z)=z+an+1zn+1+an+2zn+2+… where an+1 is fixed throughout. We provide a unified approach to radius convexity problems for different subclasses of univalent analytic functions. Numerous earlier estimates concerning the radius of convexity such as those involving fixed second coefficient, n initial gaps, n+1 symmetric gaps, etc. are discussed. It is shown that several known results, follow as special cases of those presented in this paper.