Abstract
We investigate the existence of solutions in modular function spaces of the Fredholm integral equation
Phi(theta) = g(theta) + integral(1)(0) f (theta, sigma, Phi(sigma) ) d sigma
where Phi(theta), g(theta) is an element of L-rho, theta is an element of [0, 1], f : [0, 1] x [0, 1] x L-rho -> R. An application in the variable exponent Lebesgue spaces is derived under minimal assumptions on the problem data.