# A note on the combination of equilibrium problems

## TL;DR

This paper demonstrates that the solution set of combined equilibrium problems may not be contained within the intersection of individual solution sets, challenging recent claims in the literature.

## Contribution

It provides a counterexample showing the non-inclusion property and corrects previous assertions in recent equilibrium problem research.

## Key findings

- Counterexample disproves previous inclusion claims
- Shows solution set of combined problems not necessarily in intersection
- Clarifies misconceptions in recent equilibrium problem literature

## Abstract

In this short paper, we show that the solution set of a combination of equilibrium problems is not necessary contained in the intersection of a finite family of solution sets of equilibrium problems. As a corollary, we deduce that statements in recent papers given by S. Suwannaut, A. Kangtunyakarn (Fixed Point Theory Appl. 2013, 2014; Thai Journal of Maths. 2016), W. Khuangsatung, A. Kangtunyakarn (Fixed Point Theory Appl. 2014), and A.A. Khan, W. Cholamjiak, and K.R. Kazmi (Comput. Appl. Maths. 2018) are not correct.