Subclasses of univalent functions related with functions of bounded radius rotation

Abstract

This investigation is in twofold. Firstly, a comprehensive generalization of starlike functions is initiated. This notion gives more insight to the study of functions with bounded radius rotation. In this direction, we examine the geometric characterization of this class, which includes the inclusion, radius results and integral preserving properties. On the other hand, the class of functions that extend the idea of close-toconvex functions is introduced. Also, a necessary condition, radius results, coefficient results and closure property under convex convolution for this novel class are investigated. Overall, some alluring consequences of our results are also presented.