Abstract:Since the error can be reduced effectively by using set-valued mapping instead of traditional single-valued mapping in data analysis, it is of great importance for the research into multifunctions. Previous work have discussed iterative roots of globally strict monotone upper semi-continuous multifunctions having a finte number of set-valued points. Therefore,we follow up to investigate the iterative roots of piecewise strictly increasing multifunctions with a unique set-valued point, and give the structure of iterative roots.