A fixed point result and the stability problem in Lie superalgebras

Fixexd point theory and applications

Sadegh Abbaszadeh¹  Madjid Eshaghi²  Manuel de la Sen²  Zahra Farhad³ 

[1] Center of Excellence in Nonlinear Analysis and Applications, Semnan University, Semnan, Iran;Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran;Young Researchers and Elite Club, Malayer Branch, Azad University, Malayer, Iran

关键词: Lie superalgebra;    superhomomorphism;    superderivation;    T-orbitally complete metric space;    47H10;    39B82;    16W25;   

DOI  :  10.1186/s13663-015-0469-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY