In our previous work, we have generalized the notion of dually flat or Hessian manifold to quasi-Hessian manifold; it admits metric be degenerate but possesses a particular symmetric cubic tensor (generalized Amari-Centsov tensor). Indeed, naturally appears as singular model in information geometry and related fields. A is locally accompanied with possibly multi-valued potential its dual, whose...

By using a Danes̆’ drop theorem in locally convex spaces we obtain a vectorial form of Ekelandtype variational principle in locally convex spaces. From this theorem, we derive some versions of vectorial Caristi-Kirk’s fixed-point theorem, Takahashi’s nonconvex minimization theorem, and Oettli-Théra’s theorem. Furthermore, we show that these results are equivalent to each other. Also, the existen...

Permission is herewith granted to university to circulate and to have copied for non-commercial purposes, at its discretion, the above title upon the request of individuals or institutions. to my family and to Paola vi Acknowledgements After a so great experience I obviously have many people to thank... At first, I would like to deeply thank Prof. Stefano Chiaverini, my mentor, for all he has d...

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 m...