the uniqueness of the integral equation

Question

If $x(0)=\int_{0}^{T} A(t)y(t)dt-\int_{t=0}^{T}\int_{s=0}^{t} B(t, s)f(s, x(s))\hspace{0.1 cm}ds \hspace{0.1 cm}dt,$ where $A(t),$ $B(t, s)$ are the known $n \times m$ and $n \times n$ matrices respectively, $y(t)$ and $f(s, x(s))$ are the vectors in $\mathbb{R}^m$ and $\mathbb{R}^n$ respectively. Then my question is under what conditions for each $y(t)$ the above equation has the unique value of $x(0)?$?