Systems of quasi-equilibrium problems with lower and upper bounds |
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| Affiliation: | 1. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, P.O. Box 119, Dhahran 31261, Saudi Arabia;2. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, P.O. Box 1169, Dhahran 31261, Saudi Arabia;3. Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India |
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| Abstract: | 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]. |
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