On Ekeland's variational principle for interval-valued functions with applications

Abstract

In this paper, we obtain a version of Ekeland's variational principle for interval-valued functions by means of the Dancs-Hegedüs-Medvegyev theorem (Dancs et al. (1983) [14]). We also derive two versions of Ekeland's variational principle involving the generalized Hukuhara Gâteaux differentiability of interval-valued functions as well as a version of Ekeland's variational principle for interval-valued bifunctions. Finally, we apply these new versions of Ekeland's variational principle to fixed point theorems, to interval-valued optimization problems, to the interval-valued Mountain Pass Theorem, to noncooperative interval-valued games, and to interval-valued optimal control problems described by interval-valued differential equations.