Systems of quasi-equilibrium problems with lower and upper bounds. (English) Zbl 1114.49006

Summary: We consider systems of quasi-equilibrium problems with lower and upper bounds and establish the existence of their solutions by using some known maximal element theorems for a family of multivalued maps. Our problems are more general than the one posed by G. Isac, V. M. Sehgal and S. P. Singh [Indian J. Math. 41, No. 1, 25–31 (1999; Zbl 1034.49005)]. As a particular case, we also get the answer to the problem raised by G. Isac, V. M. Sehgal, S.P. Singh [loc. cit.].


49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
91B50 General equilibrium theory


Zbl 1034.49005
Full Text: DOI


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