Resumen
We present a model involving a friction term and a delay term. By using results of existence and uniqueness for maximal monotone differential inclusions, we give theoretical results for this model. An implicit Euler numerical scheme and results related to order of convergence are also provided from both a theoretical and a numerical point of view.

Resumen
We provide and analyze an average for two convex functions, based on a kernel function. It covers several known averages such as the arithmetic average, epigraphical average, and the proximal average. When applied to the Fitzpatrick function and the conjugate of Fitzpatrick function associated with a monotone operator, our average produces an autoconjugate (also known as selfdual Lagrangian) which can be used for finding an explicit maximal monotone extension of the given monotone operator. This completely settles one of the open problems posed by Fitzpatrick in the setting of reflexive Banach spaces.