A fixed point result and the stability problem in Lie superalgebras

Abstract

In this paper, we introduce the concept of normed Lie superalgebras and define the superhomomorphism and the superderivation in normed Lie superalgebras. We define a generalized T-orbitally complete metric space and prove a new fixed point alternative concerning the stability problem of functional equations. Consequently, we deal with the stability of the superhomomorphism and the superderivation in Lie superalgebras using that new fixed point result. In addition, we find some conditions under which an approximate superhomomorphism or superderivation is an exact superhomomorphism or superderivation.