Let $f,g \in \mathcal{L}_1(\mathbb{R^n},\mathbb{K})$ if $\mathcal{N}_1 (f)<\frac{1}{|\lambda|}$ for some $\lambda \in\mathbb{K}-\{0\}$, then using fourier transform show that the integral equation $$X(x)=\int_{\mathbb{R}^n}\lambda X(y)f(x-y)dy+g(x)$$ $\forall x \in \mathbb{R}^n$ admits a unique solution $X \in \mathcal{L}_1(\mathbb{R}^n,\mathcal{K})$ except for equivalences,and tell how to find such a solution.
I have tried to occupy some isometry property of the fourier transform or something fixed point style but I have not been able to get anywhere, any suggestion or help to finish the problem I will be very grateful.