Variational Principles and Completeness in Pseudo-Quasimetric Spaces
نویسندگان
چکیده
In this paper we establish new forward and backward versions of Ekeland’s variational principle for the class of strictly-decreasing forward(resp. backward-) lower-semicontinuou functionals in pseudo-quasimetric spaces. We do not require that the space under consideration either is complete or enjoys the limit uniqueness property due to the fact that the collections of forward and backward limits of a sequence , in general, are not a singleton in a pseudo-quasimetric space. We also show that they are characterizations of forward (respectively, backward) complete pseudo-quasimetric spaces and provide examples illustrating significant improvements of the obtained results even in complete metric spaces. MSC. 49K27, 54E55, 90C30.
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