Generalized Lasry – Lions regularization function using Bregman distant

The purpose of the research is to study Bergman distance to generalize Lasry – Lions regularization which play important role of theory optimization. To do that we replace the quardatic additive terms in Lasry – Lions regularization by more general Bergman distance (non metric distance), and study properties generalized approximation and proof its continuous as we give a relationship between the solution minimization sets of function and Lions – Lasry Regularization and others properties.