Levitin-Polyak Well-posedness for Split Equilibrium Problems

TL;DR

This paper extends the concept of Levitin-Polyak well-posedness to split equilibrium problems in Banach spaces, providing a metric characterization and linking it to solution uniqueness.

Contribution

It introduces a new framework for analyzing the stability and well-posedness of split equilibrium problems in Banach spaces, including a metric characterization.

Findings

Established a metric characterization of Levitin-Polyak well-posedness.

Showed the equivalence between well-posedness by perturbations and solution uniqueness.

Extended the concept of well-posedness to split equilibrium problems in Banach spaces.

Abstract

The notion of well-posedness has drawn the attention of many researchers in the field of nonlinear analysis, as it allows to explore problems in which exact solutions are not known and/or computationally hard to compute. Roughly speaking, for a given problem, well-posedness guarantees the convergence of approximations to exact solutions via an iterative method. Thus, in this paper we extend the concept of Levitin-Polyak well-posedness to split equilibrium problems in real Banach spaces. In particular, we establish a metric characterization of Levitin-Polyak well-posedness by perturbations and also show an equivalence between Levitin-Polyak well-posedness by perturbations for split equilibrium problems and the existence and uniqueness of their solutions.