<p>In this research paper, we have introduced a Bregman-type subgradient extragradient algorithm to address pseudomonotone variational inequality problems and the fixed points of Bregman demigeneralized mappings. Leveraging the Bregman distance approach, our algorithm applies the viscosity method with an inertial parameter to approximate a common solution for a variational inequality problem and the fixed points of demigeneralized mappings in a real reflexive Banach space. Our algorithm has been carefully developed to eliminate the need for relying on the Lipschitz constant of the cost operator while incorporating an inertial extrapolation process to enhance the algorithm’s convergence rate. To demonstrate the accuracy and efficacy of our approach, we have provided two numerical examples. These results not only showcase the performance of our algorithm but also extend the previous findings in the realm of this research.</p>