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Mathematics Subject Classification: Primarios: 90C33, secundarios: 65K05.
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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.31 n.1 San José Jan./Jun. 2024
http://dx.doi.org/10.15517/rmta.v31i1.54615
Artículo
Unicidad para problemas de cuasi-equilibrio
Uniqueness for quasi-equilibrium problems
1Universidad Nacional de Ingeniería, Facultad de Ciencias, Lima, Perú; fnavarro@uni.edu.pe
2Universidad Cesar Vallejo, Facultad de Ingeniería y Arquitectura, Lima, Perú; rmitac@ucv.edu.pe
Este trabajo presenta un resultado sobre unicidad para problemas de cuasiequilibrio (QEP), que no requiere de la hipótesis de Hölder continuidad, que según nuestro conocimiento es la hipótesis sobre el cual se ha garantizado unicidad para QEP hasta la actualidad. La idea básica de nuestro enfoque consiste en iniciar con un QEP simple, por ejemplo un problema de equilibrio (EP), que denotaremos por QEP(t0) con t0 ∈ (0, 1), del cual asumiremos unicidad de la solución, bajo algunas condiciones suficientes de no-singularidad dadas por nuestras hipótesis garantizamos la existencia de un camino continuo de soluciones únicas de QEPs parametrizados que empiezan en la solución del QEP(t0) y finalizan en la solución del QEP(1) que es el QEP original. Finalmente estudiamos estas condiciones basadas en cierto tipo de matrices, para casos particulares de QEPs que son populares en la literatura.
Palabras clave: problemas de cuasi-equilibrio; unicidad; enfoque de continuación; función implícita.
This work presents a result on uniqueness for quasi-equilibrium problems (QEP), which does not require the continuity of Hölder’s hypothesis, which to our knowledge is the hypothesis on which uniqueness has been guaranteed for QEP until today. The basic idea of our approach is to start with a simple QEP, for example an equilibrium problem (EP), which we denote by QEP(t0) with t0 ∈ (0, 1), of which we will assume uniqueness of the solution, under some sufficient conditions of non-singularity given by our hypotheses we guarantee the existence of a continuous path of unique solutions of parameterized QEPs that begin in the solution of the QEP(t0) and ends in the solution of QEP(1) which is the original QEP. Finally we study these conditions based on certain types of matrices, for particular cases of QEPs that are popular in the literature.
Keywords: quasi-equilibrium problems; uniqueness; continuation approach; implicit function.
Agradecimientos
Queremos agradecer a los evaluadores de la Revista de Matemáticas: Teoría y Aplicaciones por el tiempo, comentarios y valoración que tuvieron en la revisión de nuestro artículo. Su arbitraje dio lugar a que nuestro trabajo mejorará considerablemente en calidad y contenido.
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Recibido: 13 de Junio de 2023; Aprobado: 15 de Diciembre de 2023
Este es un artículo publicado en acceso abierto bajo una licencia Creative Commons
