SUBCLASSES OF UNIVALENT FUNCTIONS RELATED WITH FUNCTIONS OF BOUNDED RADIUS ROTATION

SUBCLASSES OF UNIVALENT FUNCTIONS RELATED WITH FUNCTIONS OF BOUNDED RADIUS ROTATION

K. I. Noor, A. Saliu, M. Nasir

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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 characteri- zation 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-to- convex functions is introduced. Also, a necessary condition, radius results, coe cient results and closure property under convex convolution for this novel class are investi- gated. Overall, some alluring consequences of our results are also presented.

Keywords

Parabolic domain, Analytic functions, Subordination, Univalent functions.