Volume 34 • Number 3 • 2011   • Second-Order Differential Subordination for Analytic Functions with Fixed Initial Coefficient Rosihan M. Ali, Sumit Nagpal and V. Ravichandran Abstract. Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several interesting examples are given. The results obtained are applied to the classes of convex and starlike functions with fixed second coefficient. 2010 Mathematics Subject Classification: 30C45, 30C80. Full text: PDF