J . n . mather worked initially on this topic . then radmila bulajich brought forward the concept of relative map - germ , and solved the problem of relative versality for relative map - germs , and got the theorem of versal unfoldings of relative map - germs J . n . mather就此问题作了开创性的工作，之后radmilabulajich提出了相对映射芽的概念，解决了其相对通用开折问题，得出了相对映射芽的通用开折定理。
