Abstract
In this paper, we prove a new existence result for a system of generalized set-valued quasi-variational inclusions by using a fixed point technique.
Highlights
Xin-bo YANG and Jian-wen PENG abstract: In this paper, we prove a new existence result for a system of generalized set-valued quasi-variational inclusions by using a fixed point technique
Let F : H1 × H2 −→ H1 be strongly monotone with respect to g1 in the first argument with constant α1 > 0, Lipschitz continuous in the first argument with constant β1 > 0, and Lipschitz continuous in the second argument with constant ξ1 > 0, respectively, where g1 : H1 −→ H1 is defined by g1(x) = H1 ◦ g1(x) = H1(g1(x)), ∀x ∈ H1
Let G : H1 × H2 −→ H2 be strongly monotone with respect to g2 in the second argument with constant α2 > 0, Lipschitz continuous in the second argument with constant β2 > 0, and Lipschitz continuous in the first argument with constant ξ2 > 0, respectively, where g2 : H2 −→ H2 is defined by g2(y) = H2 ◦ g2(y) = H2(g2(y)), ∀y ∈ H2
Summary
Xin-bo YANG and Jian-wen PENG abstract: In this paper, we prove a new existence result for a system of generalized set-valued quasi-variational inclusions by using a fixed point technique. Let η : H × H −→ H be a single-valued Lipschitz continuous operator with constant τ , H : H −→ H be a strongly η-monotone operator with
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