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      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

       

      Jaeyoung Chung1 Heather Hunt2 Allison Perkins2 Prasanna K Sahoo2

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

       
  • Proceedings – Mathematical Sciences | News

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