Closedness under addition for families of quasimonotone operators

Fabián Flores-Bazán, Nicolas Hadjisavvas, Yboon García-Ramos

Producción científica: Contribución a una revistaArtículo de revista revisión exhaustiva


In the last two decades, several properties of operators that are weaker than monotonicity have received attention by researchers from many areas including mathematical economics, with the goal to develop new tools applicable in convex analysis and related topics. This paper puts in perspective notions that are extensions of monotoniticity but not beyond quasimonotonicity like pseudomonotonicity, semistrict quasimonotonicity, strict quasimonotonicity and proper quasimonotonicity, and discusses systematically when the sum of two operators satisfying one of those properties, inherits the same property. The case of properly quasimonotone operators deserves a special attention since this notion, being stronger than quasimonotonicity, suffices to obtain many results, including the solvability of variational inequality problems. Several examples showing the optimality in some sense of our results, are presented.

Idioma originalInglés
Páginas (desde-hasta)1267-1284
Número de páginas18
Fecha en línea anticipada7 dic. 2022
EstadoPublicada - 2024

Nota bibliográfica

eISSN: 1029-4945
Publisher Copyright: © 2022 Informa UK Limited, trading as Taylor & Francis Group.

Palabras clave

  • Quasiconvex function
  • Quasimonotone operator
  • Quasiconvex optimization


Profundice en los temas de investigación de 'Closedness under addition for families of quasimonotone operators'. En conjunto forman una huella única.

Citar esto