Unicidad para problemas de cuasi-equilibrio

• Navarro Rojas, Frank ^[1] ; Mitac Portugal, Raúl ^[2]
  1. [1] Universidad Nacional de Ingeniería

     Universidad Nacional de Ingeniería

     Perú

     
  2. [2] Universidad César Vallejo

     Universidad César Vallejo

     Provincia de Trujillo, Perú

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 31, Nº. 1, 2024 (Ejemplar dedicado a: Revista de Matemática: Teoría y Aplicaciones), págs. 127-151
• Idioma: español
• DOI: 10.15517/rmta.v31i1.54615
• Títulos paralelos:
  • Uniqueness for quasi-equilibrium problems
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    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.

  • English

    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.

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