The Generalized Pomeron Functional Equation

This paper investigates the linear functional equation with constant coefficients , where both and are constants, f is a given continuous function on , and is unknown. We present all continuous solutions of this functional equation. We show that (i) if , then the equation has infinite many continuous solutions, which depends on arbitrary functions; (ii) if , then the equation has a unique continuous solution; and (iii) if , then the equation has a continuous solution depending on a single parameter under a suitable condition on f.