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Some equivalent formulations of the generalized Ekeland’s variational principle and their applications. (English) Zbl 1111.49013
Summary: We first give a generalized Takahashi’s existence theorem. From the existence theorem, we establish some equivalence relations between generalized Caristi’s fixed point theorems and generalized Ekeland’s variational principles. Some applications to the existence theorems of weak sharp minima and global error bounds for lower semicontinuous functions are also given.
MSC:
49J53Set-valued and variational analysis
49J27Optimal control problems in abstract spaces (existence)