On bounded functions related to spirallike functions of complex order (Q2755574)

In this study the author is giving the coefficient inequality for the class of the bounded functions related to the spirallike functions of complex order (i.e \(S_n^\lambda (b,M))\) by using \(n\)th Ruscheweyh derivative and the method of Clunie (Theorem 2) The maximization of \(|a_3- \mu a_2^2|\) is given \((\mu\) is complex, theorem 3). Similarly by using the definition of convolution the necessary and sufficient condition is given for a function to be in \(S_n^\lambda (b,M)\) (theorem 4). Further the sufficient condition in terms of coefficient for a function to belong to \(S^\lambda_n (b<M)\). All results of this study are new.