# A generalised G\u{a}vru\c{t}a stability of cohomological equations in nonquasianalytic Carleman classes

## TL;DR

This paper introduces a generalized stability concept for functional equations within nonquasianalytic Carleman classes, focusing on the stability of cohomological equations.

## Contribution

It develops a new generalized Gavruta stability framework applicable to cohomological equations in nonquasianalytic Carleman classes.

## Key findings

- Established stability results for cohomological equations
- Extended stability concepts to nonquasianalytic Carleman classes
- Provided a theoretical foundation for future research in functional equations

## Abstract

In this paper we introduce the notion of generalized Gavr\`uta stability of functional equations in order to study, in the framework of a nonquasianalytic Carleman class, the stability of a class of cohomological equations.