Generalized Bregman Envelopes and Proximity Operators

Every maximally monotone operator can be associated with a family of convex functions, called the Fitzpatrick or representative functions. Surprisingly, in 2017, Burachik and Martínez-Legaz showed that well-known Bregman distance is particular case general distances, each one induced by specific choice its For generalized sufficient conditions for convexity, coercivity, supercoercivity have recently been furnished. Motivated these advances, we introduce present paper left right envelopes proximity operators, provide asymptotic results parameters. Certain extend readily from more context, while others only certain cases. To illustrate, construct examples generalizing case, together natural “extreme” cases highlight importance which chosen.