Coefficient estimates for certain subclasses of biunivalent functions defined by convolution (Q502596)

Summary: We introduce two new subclasses of the function class \(\Sigma\) of biunivalent functions in the open disc defined by convolution. Estimates on the coefficients \(|a_2|\) and \(|a_3|\) for the two subclasses are obtained. Moreover, we verify Brannan and Clunie's conjecture \(|a_2| \leq \sqrt{2}\) for our subclasses.