In this thesis, we study the approximation of continuous functions in Banach spaces. We will prove that if is a infinite-dimensional Banach space with separable dual then every continuous function can be uniformly approximated by a mooth function which does not have any critical point. Also state sufficient conditional on separable Banach space o that the approximating function can be taken to be of o:ole="" type="#_x0000_t75" , for ,
