In this paper, we introduce some new concepts, and study random solution of random operator equation of 1 set contractive type.

In this paper, to 1-set contraction random operator equation, the author explained the conception of couple solution, obtained existence theorem of couple solution.

In this paper the concept of operators of type (JM) is introduced and the existence theorems for nonlinear random operator equations of accretive type and of type (JM) are proved.