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Order-Preservation Properties of Solution Mapping for Parametric Equilibrium Problems and Their Applications

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  • Yuehu Wang

    (Nanjing University of Finance and Economics)

  • Baoqing Liu

    (Nanjing University of Finance and Economics)

Abstract

In this paper, we use some order-theoretic fixed point theorems to study the upper order-preservation properties of solution mapping for parametric equilibrium problems. In contrast to lots of existing works on the behaviors of solutions to equilibrium problems, the topic of the order-preservation properties of solutions is relatively new for equilibrium problems. It would be useful for us to analyze the changing trends of solutions to equilibrium problems. In order to show the applied value and theoretic value of this subject, we focus on a class of differential variational inequalities, which are currently receiving much attention. By applying the order-preservation properties of solution mapping to variational inequality, we investigate the existence of mild solutions to differential variational inequalities. Since our approaches are order-theoretic and the underlying spaces are Banach lattices, the results obtained in this paper neither require the bifunctions in equilibrium problems to be continuous nor assume the Lipschitz continuity for the involved mapping in ordinary differential equation.

Suggested Citation

  • Yuehu Wang & Baoqing Liu, 2019. "Order-Preservation Properties of Solution Mapping for Parametric Equilibrium Problems and Their Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 881-901, December.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:3:d:10.1007_s10957-019-01579-8
    DOI: 10.1007/s10957-019-01579-8
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    References listed on IDEAS

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    1. Li, S.J. & Chen, C.R. & Li, X.B. & Teo, K.L., 2011. "Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems," European Journal of Operational Research, Elsevier, vol. 210(2), pages 148-157, April.
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    4. Hiroki Nishimura & Efe A. Ok, 2012. "Solvability of Variational Inequalities on Hilbert Lattices," Mathematics of Operations Research, INFORMS, vol. 37(4), pages 608-625, November.
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