We study the appearance of Keplerian accretion disks in order to demonstrate the influence of the nonlinear electrodynamics (NED) on the gravitational lensing and frequency shifting of the images of the Keplerian disks. We focus our attention on the Bardeen black hole backgrounds with magnetic charges that could be considered to be acceptable solutions for the Einstein gravitational equations combined with those representing an NED. Photons governing the appearance of the Keplerian disks follow null geodesics of the effective geometry related to the Bardeen spacetime. We compare the appearance governed by the effective geometry to those governed by the spacetime geometry itself, and to the appearance of Keplerian disks orbiting a related Reissner-Nordstrom black hole spacetime. We demonstrate a clear and very strong difference between the disk images determined by the effective geometry and the others, both in the shape and (especially) in the frequency mapping where it exhibits a difference of three orders.