Variational-Like Inequality Problems Involving Set-Valued Maps and Generalized Monotonicity

Nicuşor Costea (), Daniel Alexandru Ion () and Cezar Lupu ()
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Nicuşor Costea: Institute of Mathematics “Simion Stoilow” of the Romanian Academy
Daniel Alexandru Ion: University of Craiova
Cezar Lupu: University of Craiova

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 1, No 4, 79-99

Abstract: Abstract The aim of this paper is to establish existence results for some variational-like inequality problems involving set-valued maps, in reflexive and nonreflexive Banach spaces. When the set K, in which we seek solutions, is compact and convex, we no dot impose any monotonicity assumptions on the set-valued map A, which appears in the formulation of the inequality problems. In the case when K is only bounded, closed, and convex, certain monotonicity assumptions are needed: We ask A to be relaxed η-α monotone for generalized variational-like inequalities and relaxed η-α quasimonotone for variational-like inequalities. We also provide sufficient conditions for the existence of solutions in the case when K is unbounded, closed, and convex.

Keywords: Variational-like inequalities; Generalized variational-like inequalities; Set-valued maps; Generalized monotonicity; Lower and upper semicontinuity (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-012-0047-0

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