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Certain theorems involving differential superordination and sandwich-type results
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Abstract. To obtain the main result of the present paper, we use the technique of differential superordination. As special cases of our main result, we obtain sufficient conditions for f ∈ A to be φ−like, parabolic φ−like, starlike, parabolic starlike, close-to-convex and uniform close-to-convex. We also obtain sandwich-type results regarding these functions. For demonstration of the results, we have plotted the images of open unit disk under certain functions using Mathematica 7.0.
Mathematics Subject Classification (2010): 30C80, 30C45.
Keywords: Analytic function, differential superordination, φ−like function, starlike function, close-to-convex function.
Babes-Bolyai University Cluj-Napoca
Title: Certain theorems involving differential superordination and sandwich-type results
Description:
Abstract.
To obtain the main result of the present paper, we use the technique of differential superordination.
As special cases of our main result, we obtain sufficient conditions for f ∈ A to be φ−like, parabolic φ−like, starlike, parabolic starlike, close-to-convex and uniform close-to-convex.
We also obtain sandwich-type results regarding these functions.
For demonstration of the results, we have plotted the images of open unit disk under certain functions using Mathematica 7.
Mathematics Subject Classification (2010): 30C80, 30C45.
Keywords: Analytic function, differential superordination, φ−like function, starlike function, close-to-convex function.
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