Systems of quasi-equilibrium problems with lower and upper bounds

• Published in: Applied mathematics letters Vol. 20; no. 3; pp. 323 - 328
• Main Authors: Al-Homidan, Suliman, Ansari, Qamrul Hasan
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.2007; Elsevier
• Subjects: Exact sciences and technology; Global analysis, analysis on manifolds; Lower and upper bounds; Mathematics; Maximal element theorems; Sciences and techniques of general use; System of generalized implicit quasi-equilibrium problems; System of quasi-equilibrium problems; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Maximal element theorems; System of quasi-equilibrium problems; System of generalized implicit quasi-equilibrium problems; Lower and upper bounds; Lower bound; Upper bound; Maximal element theorem; Existence of solution; Applied mathematics
• ISSN: 0893-9659; 1873-5452
• DOI: 10.1016/j.aml.2006.04.016

In this work, 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 in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31]. As a particular case, we also get the answer to the problem raised in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31].