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In this paper, we consider the implicit quasi-variational inequality without continuity assumptions of data mappings. Our approach here is completely different from the one based on KKM theorem in the literature. Interesting applications to generalized quasi-variational inequalities for both discontinuous mappings and discontinuous fuzzy mappings are given.
|In this paper, we consider the general nonlinear variational inequality introduced in the paper 1], which extends several variational problems in the literature arising from mechanics, physics, and engineering. Some new existence results are established in the setting of real reeexive Banach spaces for the case where the main operator satisses a condition… (More)
We consider the integral equation h(u(t)) = f R I g(t, x)u(x) dx , with t ∈ [0, 1], and prove an existence theorem for bounded solutions where f is not assumed to be continuous.
We deal with the integral equation u(t) = f(t, R I g(t, z)u(z) dz), with t ∈ I := [0, 1], f : I × R → R and g : I × I → [0,+∞[. We prove an existence theorem for solutions u ∈ L(I,R), s ∈ ]1,+∞], where f is not assumed to be continuous in the second variable. Our result extends a result recently obtained for the special case where f does not depend… (More)
We deal with the integral equation u(t) = f( R I g(t, z)u(z) dz), with t ∈ I = [0, 1], f : R → R and g : I×I → [0,+∞[. We prove an existence theorem for solutions u ∈ L(I,R) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1.
We establish a fixed point theorem for a continuous function f : X → E, where E is a Banach space and X ⊆ E. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.