A Further Study on Asymptotic Functions via Variational Analysis

  • Felipe LaraEmail author
  • Rubén López
  • Benar F. Svaiter


We use variational analysis for studying asymptotic (recession or horizon) functions. We introduce the upper and lower asymptotic operators and study their domain and image. Moreover, we characterize their fixed points and zeros. Finally, we establish continuity properties of this operator, i.e., the convergence of asymptotic functions of convergent sequences of functions.


Asymptotic functions Variational analysis Operator theory Set convergence Epi-convergence 

Mathematics Subject Classification

90C25 90C26 90C31 



The authors want to express their gratitude to the referees for their criticism and suggestions that helped to improve the paper. This research was partially supported by Conicyt-Chile throughout Projects Fondecyt Iniciación 11180320 (Lara) and Fondecyt Regular 1181368 (López), by Universidad de Tarapacá throughout project UTA-Mayor 4739-18 (López) and by Conselho Nacional de Desenvolvimento Científico e Tecnológico Grant 306247/2015-1 and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro Grant Cientistas de Nosso Estado E-26/201.584/2014 (Svaiter).


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Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad de TarapacáAricaChile
  2. 2.Instituto Nacional de Matemática Pura e Aplicada (IMPA)Rio de JaneiroBrazil

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