Conversion of meromorphic functions to close to convex functions

We give general relations about starlike and convex of the derivatives of a meromorphic function in the unit disk with the help of the ordinary derivative operator and to find some relations on the starlike and convex of these function. For this, firstly, the concepts related to the starlike and convex of univalent functions in the unit disk were introduced, and then studies were carried out on the conditions under which a univalent function is starlike and convex, close to convex and what kind of relations there are between starlike, convex and close to convex. These properties of analytic and univalent meromorphic functions in the drilled unit disk and the necessary and sufficient conditions for these functions to be starlike and convex are investigated. Moreover it is mentioned that meromorphic functions are univalent functions that are analytical everywhere. Complex analytic transformations were investigated by mentioning the necessary form for f(z) to have meromorphic function. It is a function f(z)=g(z)/h(z) that satisfies the condition h(z) not equal zero. For analytic functions of f and g in the unit disk D, shows the meromorphic function class M with and subclasses of M_a,_b(alpha,beta;h) the meromorphic analytical function class using the subordination principle between functions with the help of Hadamard product and linear operators. In this way proves is provided. Finally, conclusions and recommendations are given.