Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

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Uniqueness for quasi-equilibrium problems
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Keywords

Problemas de cuasi-equilibrio
Unicidad
Enfoque de continuación
Función implícita
Quasi-equilibrium problems
Uniqueness
Continuation approach
Implicit function

How to Cite

Navarro Rojas, F. ., & Mitac Portugal, R. . (2024). Uniqueness for quasi-equilibrium problems. Revista De Matemática: Teoría Y Aplicaciones, 31(1), 127–151. https://doi.org/10.15517/rmta.v31i1.54615

Abstract

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.

https://doi.org/10.15517/rmta.v31i1.54615
PDF (Español (España))

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Copyright (c) 2024 Frank Navarro Rojas, Raúl Mitac Portugal

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