New Criteria for Univalent‎, ‎Starlike‎, ‎Convex‎, ‎and Close-to-Convex Functions on the Unit Disk

Abstract

In the present paper, we introduce and investigate three interesting superclasses SD, SD* and KD of analytic, normalized and univalent functions in the open unit disk D. For functions belonging to these classes SD, SD* and KD, we derive several properties including (for example) the coefficient bounds and growth theorems. The various results presented here would generalize many well known results. We also get a new univalent criterion and some interesting properties for univalent function,starlike function,convex function and close-to-convex function. Many superclasses which are already studied by various researchers are obtained as special cases of our two new superclasses.

Keywords

• univalent functions
• starlike functions
• convex functions
• close-to-convex function