New properties of the generalized Dini function

In this work we study some properties of the normalized form of generalized Dini function like close-to-convexity of some order and close-to-convex with respect to another convex function. Furthermore, we investigate sufficient conditions which these functions are uniformly $k$-starlike functions of complex order $b$ in the open unit disk, and some consequences of the main results are also presented. ****************************************************************************************************************************