On Hölder continuity of approximate solutions to parametric equilibrium problems

We establish verifiable sufficient conditions for Hölder continuity of approximate solutions to parametric equilibrium problems, when solutions may be not unique. Many examples are provided to illustrate the need of considering approximate solutions instead of exact solutions and the essentialness o...

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Bibliographic Details
Published in:Nonlinear analysis 2012-03, Vol.75 (4), p.2293-2303
Main Authors: Anh, L.Q., Khanh, P.Q., Tam, T.N.
Format: Article
Language:English
Subjects:
Approximate solutions
Approximation
Concavity
Constrained minimization
Continuity
Exact solutions
Fixed point problems
Hölder continuity
Inequalities
Mathematical analysis
Minimization
Nonlinearity
Optimization
Parametric equilibrium problems
Variational inequalities
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Summary:We establish verifiable sufficient conditions for Hölder continuity of approximate solutions to parametric equilibrium problems, when solutions may be not unique. Many examples are provided to illustrate the need of considering approximate solutions instead of exact solutions and the essentialness of the imposed assumptions. As applications, we derive this Hölder continuity for constrained minimization, variational inequalities and fixed point problems.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2011.10.029