  In this paper, I investigate the nonlinear magnetized black holes of massive
gravity's rainbow. In order to achieve this, I use the double-logarithmic
electromagnetic field as a matter source and derive the new anti-de Sitter
black hole solution. The effects of the massive graviton, rainbow functions,
and nonlinearity of the electromagnetic field on the black hole's inner and
outer horizons are also studied. The black hole's thermodynamic properties are
studied, and the mathematical expressions for temperature, heat capacity, and
Gibbs free energy are found. The extended first law and Smarr's formula are
derived as well. Using the behaviour of thermodynamic quantities as a starting
point, I also study the local and global thermodynamic stabilities.
