in this thesis we will present three topics. we define approximate fixed points in fuzzy normed spaces. also we obtain some necessary and sufficient conditions on the existence of? -fixed points for ? > 0. at the continue some results about approximate fixed points for a class of non-expansive maps on g-metric spaces are obtained and we define approximate fixed points in partial metric spaces. also, ? -pair proximity for one and two maps and the relations between ? -pair proximities and fixed points will be studied. at the end, we show that approximate best proximity pairs can be applied for proving the existence of the approximate solutions for integral and ordinary differential equations.