Hyperstability of an alternative equation of Jensen type

Abstract

We studied the stability and hyperstability of the alternative functional equationfor all x, y ∈ G using an algebraic approach. The functions are defined as f : G → B where G is a commutative group and B is a Banach space with λ / ∈ {−2, −1, 0, 2}. We have obtained some necessary conditions on which sufficient conditions for hyperstability were established.