%0 Journal Article %T The solutions of four $q$-functional equations %A Jun-Ming Zhu %J Mathematics %D 2010 %I arXiv %X In this note we obtain the solutions of four $q$-functional equations and express the solutions in $q$-operator forms. These equations give sufficient conditions for $q$-operator methods. %U http://arxiv.org/abs/1001.0299v1