I am currently trying to solve a set of integral equations of the form
\begin{equation} \ln \int^1_0 f(s, t) \ \text{d}s = b + \int_0^1 w(t, s) \ \ln f(t, s) \ \text{d}s, \end{equation}
where $b \in \mathbb{R}$, for $f$ in the set of 1-periodic functions, $[0, 1] \to \mathbb{R}$ with $f(s, t) = f(s, t + 1) = f(s + 1, t)$.
I am reading Masujima's Applied Mathematical Methods of Theoretical Physics but could not find a solution to this class of equations. Do you know of any solution to these or can you point me to some paper/book that my work on similar problems?
Thank you!