Discontinuous implicit generalized quasi-variational inequalities in Banach spaces |
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Authors: | Paolo Cubiotti Jen-chih Yao |
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Institution: | (1) Department of Mathematics, University of Messina, Contrada Papardo, Salita Sperone 31, 98166 Messina, Italy;(2) Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan R.O.C |
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Abstract: | We consider the following implicit quasi-variational inequality problem: given two topological vector spaces E and F, two nonempty sets X
E and C
F, two multifunctions Γ : X → 2
X
and Ф : X → 2
C
, and a single-valued map ψ :
, find a pair
such that
,
Ф
and
for all
. We prove an existence theorem in the setting of Banach spaces where no continuity or monotonicity assumption is required
on the multifunction Ф. Our result extends to non-compact and infinite-dimensional setting a previous results of the authors
(Theorem 3.2 of Cubbiotti and Yao 15] Math. Methods Oper. Res. 46, 213–228 (1997)). It also extends to the above problem a recent existence result established for the explicit case (C = E
* and
). |
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Keywords: | Implicit generalized quasi-variational inequalities Multifunctions Lower semicontinuity Upper semicontinuity Banach space |
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