Argument inequalities for certain analytic functions
Let q be analytic in the open unit disk U with q(0) = 1 and q(z) not equal 0 (z is an element of U). By using the method of differential subordinations, we derive certain conditions involving q and zq' under which the functions q satisfy the following two-sided inequality: alpha(2)pi/2 < argq(z) alpha(1)pi/2 (z is an element of U) for some alpha(1) and alpha(2) (0 < alpha(1), alpha(2) <= 1). Several interesting consequences of the main results are also given. All these results presented here are sharp. (C) 2010 Elsevier Ltd. All rights reserved.
analytic functions subordination multivalent functions starlike functions strongly starlike functions close-to-convex functions