The Product Formula and Evolution Families of Nonexpansive Mappings

In this work we obtain a product formula type for a two-parameters commuting family of nonexpansive mappings on D . This is established by following the techniques used by Simeon Reich and David Shoikhet in the study of one-parameter semigroups of holomorphic and nonexpansive self-mappings in D . Also, we stablish such a formula for the family of non-linear resolvent of a strongly ρ -monotone functions on D and its relation with evolution families of nonexpansive mappings on D . It is worthy mentioning that the product formula is linked with semigroup of linear and nonlinear operators. Also it is associated with the study of vector fields and flows, but in the literature it is established a product formula for time independent flow.