Defective functions of meromorphic functions in the unit disc

Abstract

Abstract Let f be a meromorphic function in the unit disc and ( a ν ) ν = 1 k ${(a_\nu )_{\nu =1}^k}$ a set of distinct meromorphic functions small with respect to f. An analogue of the second main theorem for f and ( a ν ) ν = 1 k ${(a_\nu )_{\nu =1}^k}$ is given. Upper limits for the sum of defects of an admissible meromorphic function and an admissible holomorphic function follow. For meromorphic and holomorphic functions in the unit disc and their small functions the analogues of Ullrich's theorem are presented.