Sufficient conditions for close-to-convexity of an analytic function in the unit disc

Abstract

Recently C. Ramesha and others have derived a sufficient condition for functions analytic in the unit disc to be starlike. Subsequently M. Nunokowa and others have improved the earlier results of C. Ramesha and others. In this paper we generalise the results of C. Ramesha and others in a different direction and obtain sufficient conditions for $f(z)$ to be close-to-convex in the unit disc $E$.