Certain theorems involving differential superordination and sandwich-type results

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.