Geodesic
Second-Order Differential Subordination for Analytic Functions with Fixed Initial Coefficient
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 3 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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.
Classification : 30C45, 30C80. 
@article{BMMS_2011_34_3_a17,
     author = {Rosihan M. Ali and Sumit Nagpal and V. Ravichandran},
     title = {Second-Order {Differential} {Subordination}  for {Analytic} {Functions} with {Fixed} {Initial} {Coefficient}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2011},
     volume = {34},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2011_34_3_a17/}
}
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Rosihan M. Ali; Sumit Nagpal; V. Ravichandran. Second-Order Differential Subordination  for Analytic Functions with Fixed Initial Coefficient. Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2011_34_3_a17/