A Minimization Theorem in Quasi-metric Spaces and Its Applications

  title={A Minimization Theorem in Quasi-metric Spaces and Its Applications},
  author={Jeong Sheok Ume},
We prove a new minimization theorem in quasi-metric spaces, which improves the results of Takahashi (1993). Further, this theorem is used to generalize Caristi's fixed point theorem and Ekeland's ε-variational principle. 1. Introduction. Caristi [1] proved a fixed point theorem on complete metric spaces which generalizes the Banach contraction principle. Ekeland [3] also obtained a non-convex minimization theorem, often called the ε-variational principle, for a proper lower semicontinuous… CONTINUE READING
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