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Additive s-functional inequality and hom-derivations in Banach algebras

  • Choonkil Park
  • Jung Rye LeeEmail author
  • Xiaohong Zhang
Article
  • 57 Downloads

Abstract

In this paper, we introduce and solve the following additive s-functional inequality:
$$\begin{aligned} \left\| f\left( x+y\right) - f(x )- f(y)\right\| \le \Vert s (f(x-y)-f(x)-f(-y))\Vert , \end{aligned}$$
(0.1)
where s is a fixed nonzero complex number with \(|s|<1\). Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of the additive s-functional inequality (0.1) in complex Banach spaces. Furthermore, we prove the Hyers–Ulam stability of hom-derivations in complex Banach algebras.

Keywords

Hyers–Ulam stability hom-derivation in Banach algebra additive s-functional inequality fixed point method direct method 

Mathematics Subject Classification

Primary 39B62 47H10 39B52 47B47 46L57 

Notes

Acknowledgements

This research was supported by the Daejin University Research Grant.

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Authors and Affiliations

  1. 1.Research Institute for Natural SciencesHanyang UniversitySeoulRepublic of Korea
  2. 2.Department of MathematicsDaejin UniversityKyunggiRepublic of Korea
  3. 3.Department of Mathematics, School of Arts and SciencesShaanxi University of Science and TechnologyXi’anPeople’s Republic of China
  4. 4.Department of Mathematics, College of Arts and SciencesShanghai Maritime UniversityShanghaiPeople’s Republic of China

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