# unicity of Cauchy problem-fixed point

Let the problem $$y' = f(x,y) , y(x_0) = y_0$$ Let $f$ an continuous function, bounded on $R = \{(x,y) \in \mathbb{R}^2, |x-x_0| \leq a , |y-y_0| \leq b\}$ such that $f$ is Lipschitz compared with $y.$

How we can use the fixed point method to prouve that this Cachy problem admits a unique solution?