COCYCLE EQUATIONS VIA COCHAINS AND HYPERSTABILITY OF RELATED FUNCTIONAL EQUATIONS

Abstract

This paper presents properties of the cocycle equations via cochains on a semi-group. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can beapplied to obtain hyperstability of various functional equations such as Euler-Lagrange typequadratic equations.