Let L(f, r) denote the length of the closed curve which is the image of |z| = r < 1 under the mapping w = f(z). We establish some sufficient conditions for L(f, r) to be bounded and for f(z) to in the classes of strongly close-to-convex function of order α and to be strongly Bazilevič function of type β of order α. Moreover, we prove an inequality connected with the Fejér-Riesz's inequality.
The purpose of this work is to present a new geometric approach to some problems in differential subordination theory. We also discuss the new results closely related to the generalized Briot-Bouquet differential subordination.
Authors:Poonam Sharma, Ravinder Krishna Raina, and Janusz Sokół
In this paper, a class Ss(q) of close-to-convex functions is considered. Among the results studied for this class are its various characteristic properties such as the radius of convexity, certain bounds and coeffcient estimates. A suffcient condition for a function f to be in the class Ss(q), is also obtained.