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In this paper, we give an example and point out that ϵ-solutions of Ekeland's variational principle are not always lower semicontinuous in infinite-dimensional Banach spaces, even with respect to the uniform metric. Further, the example shows that the ϵ-solutions need not be almost lower semicontinuous when the convergence of sequence of functions is weakened to Painlevé–Kuratowski epigraphical convergence...
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