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

• # Fulltext

Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/124/03/0365-0381

• # Keywords

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

• # Abstract

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 $|f(x+y)-f (x)h(y)-f(y)|\leq \epsilon$ and $|f(x+y)-g(x)h(y)-k(y)|\leq \epsilon$, respectively. We also study the bounded solutions of the simple Levi–Civitá functional inequality.

• # Author Affiliations

1. Department of Mathematics, Kunsan National University, Kunsan 573-701, Korea
2. Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, USA

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019

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