Stability of a Simple Levi–Civitá Functional Equation on Non-Unital Commutative Semigroups

Proceedings Mathematical Sciences

Allison Perkins¹  Heather Hunt³  Jaeyoung Chung²  Prasanna K Sahoo¹ 

[1] $$;Department of Mathematics, Kunsan National University, Kunsan -0, Korea$$;Department of Mathematics, University of Louisville, Louisville, Kentucky 0, USA$$

关键词: Additive function;    exponential function;    functional inequality;    Hyers–Ulam stability;    Levi–Civitá equation;    non-unital semigroup;    2-divisible group.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, we study the Hyers–Ulam stability of a simple Levi–Civitá functional equation $f(x+y)=f(x)h(y)+f(y)$ and its pexiderization $f(x+y)=g(x) h(y)+k(y)$ on non-unital commutative semigroups by investigating the functional inequalities $|f(x+y)-f (x)h(y)-f(y)|≤ epsilon$ and $|f(x+y)-g(x)h(y)-k(y)|≤ epsilon$, respectively. We also study the bounded solutions of the simple Levi–Civitá functional inequality.

【 授权许可】

Unknown