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

TL;DR

This paper extends Ekeland's variational principle to interval-valued functions, providing new theoretical tools and applications in fixed point theory, optimization, game theory, and control problems involving interval data.

Contribution

It introduces novel versions of Ekeland's variational principle for interval-valued functions using the Dancs-Hegedus-Medvegyev theorem and generalized Hukuhara Gateaux differentiability.

Findings

Established Ekeland's variational principle for interval-valued functions.

Derived applications to fixed point theorems and optimization problems.

Extended results to interval-valued differential equations and game theory.

Abstract

In this paper, we obtain a version of Ekeland's variational principle for interval-value functions by means of the Dancs-Hegedus-Medvegyev theorem [14]. We also derive two versions of Ekeland's variational principle involving the generalized Hukuhara Gateaux 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.