Properties of higher order differential polynomials generated by solutions of complex differential equations in the unit disc

Throughout this paper, we assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna’s value distribution theory on the complex plane and in the unit disc ∆ = {z : |z| < 1} (see [13] , [14] , [18] , [20]). We need to give some definitions and discussions. Firstly, let us give two definitions about the degree of small growth order of functions in ∆ as polynomials on the complex plane C. There are many types of definitions of small growth order of functions in ∆ (see [10] , [11]) .