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

Document Type : Original Scientific Paper


1 Department of Mathematics, Payame Noor University, Tehran, Iran.

2 ‎Department of Mathematics, ‎Faculty of Science,‎ Urmia University, ‎Urmia‎, ‎Iran


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.


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