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Upper order-preservation of the solution correspondence to vector equilibrium problems. (English) Zbl 1434.49005
Summary: In this paper, several order-theoretic fixed point theorems are proved on partially ordered topological spaces. Applying these fixed point theorems, we explore the existence and upper order-preservation for parametric vector equilibrium problems. In contrast to the previous results on vector equilibrium problems, the upper order-preservation of solutions is a new subject, which would be useful for predicting the changing trend of solutions to vector equilibrium problems. In addition, neither topological continuity nor convexity of the considered vector-valued bifunction $$F$$ is required in our results.
MSC:
 49J40 Variational inequalities 47H10 Fixed-point theorems 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C48 Programming in abstract spaces 91B50 General equilibrium theory
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References:
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