Addendum to the paper "Refined criteria toward boundedness in an attraction-repulsion chemotaxis system with nonlinear productions"

These notes aim to provide a deeper insight on the specifics of the paper “Refined criteria toward boundedness in an attraction-repulsion chemotaxis system with nonlinear productions” by A. Columbu, S. Frassu and G. Viglialoro [$\mathit{\text{Appl.}}\mathit{\text{Anal.}}$ 2024, 103:2, 415–431].