Using topological degree for upper semicontinuous set-valued 1-set-contractive mapping and the fixed point theorems for upper semicontinuous set-valued 1-set-contractive mapping, the boundary conditions of existing positive fixed points is studied for upper semicontinuous set-valued 1-set-contractive mapping. In fact, it is a natural conclusion in the cone for the fixed point theorems of upper semicontinuous set-valued 1-set-contractive mapping, and it is a natural extend for positive fixed point theorems of single-valued 1-set-contractive mapping.