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Li, Jinlu; Ok, Efe A.

Optimal solutions to variational inequalities on Banach lattices. (English) Zbl 1231.49011

J. Math. Anal. Appl. 388, No. 2, 1157-1165 (2012).
Summary: We study the existence of maximum and minimum solutions to generalized variational inequalities on Banach lattices. The main tools of analysis are the variational characterization of the generalized metric projection operator and order-theoretic fixed point theory.

Cited in 20 Documents

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)

Keywords:

variational inequalities; Banach lattices; metric projections; fixed points
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\textit{J. Li} and \textit{E. A. Ok}, J. Math. Anal. Appl. 388, No. 2, 1157--1165 (2012; Zbl 1231.49011)
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References:

[1] Alber, Ya., Metric and generalized projection operators in Banach spaces: properties and applications, (Kartsatos, A., Theory and Applications of Nonlinear Operators of Monotonic and Accretive Type (1996), Marcel Dekker: Marcel Dekker New York), 15-50 · Zbl 0883.47083
[2] Borwein, J.; Dempster, M., The linear order complementarity problem, Math. Oper. Res., 14, 534-558 (1989) · Zbl 0692.90096
[3] Chitra, A.; Subrahmanyam, P., Remarks on nonlinear complementarity problem, J. Optim. Theory Appl., 53, 297-302 (1987) · Zbl 0595.90089
[4] Fujimoto, T., An extension of Tarskiʼs fixed point theorem and its application to isotone complementarity problems, Math. Programming, 28, 116-118 (1984) · Zbl 0526.90084
[5] Hartman, P.; Stampacchia, G., On some nonlinear elliptic differential functional equations, Acta Math., 115, 153-188 (1966) · Zbl 0142.38102
[6] Isac, G., On the order monotonicity of the metric projection operator, (Singh, S. P., Approximation Theory, Wavelets and Applications (1995), Kluwer: Kluwer Dordrecht) · Zbl 0848.46008
[7] Li, J., The generalized projection operator on reflexive Banach spaces and its applications, J. Math. Anal. Appl., 306, 55-71 (2005) · Zbl 1129.47043
[9] Meyer-Nieberg, P., Banach Lattices, Universitext (1991), Springer-Verlag · Zbl 0743.46015
[11] Ok, E. A., Order theory (2011)
[12] Takahashi, W., Nonlinear Functional Analysis (2000), Yokohama Publishers
[13] Topkis, D., Supermodularity and Complementarity (1998), Princeton University Press
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