The Product Formula and Evolution Families of Nonexpansive Mappings

  • Luis Benítez-Babilonia
  • Nancy LópezEmail author
  • Raúl Felipe


In this work we obtain a product formula type for a two-parameters commuting family of nonexpansive mappings on \({\mathbb {D}}\). 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 \({\mathbb {D}}\). Also, we stablish such a formula for the family of non-linear resolvent of a strongly \(\rho \)-monotone functions on \({\mathbb {D}}\) and its relation with evolution families of nonexpansive mappings on \({\mathbb {D}}\). 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.


Product formula Evolution families Nonlinear resolvent \(\rho \)-monotone vector fields 

Mathematics Subject Classification

47H09 30L99 30J99 37C10 37L05 



This research is supported by the Research Project (Acta no. 112015), and by the Universidad de Antioquia under SUI Research Project Dos problemas relacionados con el Control en espacios de Hilbert y en el espacio \(N_{\rho }({\mathbb {D}})\) (Acta no. 701, 2015-03-11). Raúl Felipe thanks support from CONACYT, grant 222870.


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Copyright information

© Sociedade Brasileira de Matemática 2018

Authors and Affiliations

  • Luis Benítez-Babilonia
    • 1
  • Nancy López
    • 2
    Email author
  • Raúl Felipe
    • 3
  1. 1.Departamento de Matemáticas y EstadísticasUniversidad de CórdobaMonteríaColombia
  2. 2.Instituto de MatemáticasUniversidad de AntioquiaMedellínColombia
  3. 3.Centro de Investigación en Matemáticas, A. C.GuanajuatoMexico

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