A note on an integrated Cauchy functional equation
The following equation \(f(x)=\int^{\infty}_{0}f(x+y)d\mu (y),\quad a.e.\quad x\geq 0,\) where \(\mu\) is a positive regular Borel measure defined in (0,\(\infty)\), called an integrated Cauchy functional equation, is discussed in order to establish its relevant nonnegative locally integrable solutions in (0,\(\infty)\).
nonnegative locally integrable solutions
scientific article; zbMATH DE number 4124294
scientific article