How to show the solution so this Fredholm integral is unique?
The equation
$$f(x)=g(x)+\int _0 ^1 k(x,y) f(y) \, dy$$ is equivalent to
$$f=g +Kf.$$
Hence $(I-K)f=g$. Since $I-K$ is invertble, we get
$$f=(I-K)^{-1}g.$$
How to show the solution so this Fredholm integral is unique?
The equation
$$f(x)=g(x)+\int _0 ^1 k(x,y) f(y) \, dy$$ is equivalent to
$$f=g +Kf.$$
Hence $(I-K)f=g$. Since $I-K$ is invertble, we get
$$f=(I-K)^{-1}g.$$