Lower semicontinuity of solution mappings for parametric fixed point problems with applications

TL;DR

This paper proves the lower semicontinuity of solution mappings in parametric fixed point problems, with applications to equilibrium problems and game theory, enhancing understanding of solution stability under parameter changes.

Contribution

It establishes lower semicontinuity results for solution mappings in parametric fixed point problems, extending to applications in equilibrium problems and Stackelberg games.

Findings

Solution mappings are lower semicontinuous under certain conditions.

Application to parametric vector quasi-equilibrium problems.

Existence of solutions for generalized Stackelberg games proved.

Abstract

In this paper, we establish the lower semicontinuity of the solution mapping and of the approximate solution mapping for parametric fixed point problems under some suitable conditions. As applications, the lower semicontinuity result applies to the parametric vector quasi-equilibrium problem, and allows to prove the existence of solutions for generalized Stackelberg games.