A function analytic and locally univalent in a simply connected domain is of bounded radius rotation if its range has bounded radius rotation which is defined as the total variation of the direction angle of the radial vector to the boundary curve under a complete circuit. In this paper, we introduce some subclasses of analytic functions with bounded radius rotation involving subordination and establish integral and convolution preserving properties. We also determine estimates for the growth and distortion bounds, inclusions, conditions for starlikeness and bounds on coefficients differences. Most of our findings are related with the existing known results and several of their applications are found in literature of the subject.
In this paper, we study some radii problems for certain classes of analytic functions. These results generalize some of the previously known radii problems such as the radius of convexity for starlikness and radius of quasi-convexity for close-to-convex functions. Also, it is shown that some of these radii are best possible.
In this paper, we introduce and investigate a new class of p-valent harmonic starlike functions of complex order b. We study various properties of this class including coefficient conditions, distortion bounds, extreme points, convex combination and find their connection with the already known classes.Mathematics Subject Classification: Primary: 30C45, Secondary 31A05
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