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Fixed points and partial multipliers in Banach algebras

  • Inho Hwang
  • Choonkil ParkEmail author
Article
  • 22 Downloads

Abstract

In this paper, we solve the additive functional inequalities
where s is a fixed nonzero complex number with \(|s|<1\). Using the fixed point method, we prove the Hyers–Ulam stability of the additive functional inequalities (1) and (2) in complex Banach spaces. This is applied to investigate partial multipliers in Banach \(*\)-algebras, unital \(C^*\)-algebras, Lie \(C^*\)-algebras, \(JC^*\)-algebras and \(C^*\)-ternary algebras, associated with the additive functional inequalities (1) and (2).

Keywords

Partial multiplier fixed point method; \(C^*\)-algebra Hyers–Ulam stability additive functional inequality \(C^*\)-ternary algebra Lie \(C^*\)-algebra \(JC^*\)-algebra 

Mathematics Subject Classification

Primary 39B52 46L05 47H10 39B62 43A22 

Notes

Acknowledgements

This work was supported by Incheon National University Research Grant 2018-2019.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.

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Authors and Affiliations

  1. 1.Department of MathematicsIncheon National UniversityIncheonSouth Korea
  2. 2.Research Institute for Natural SciencesHanyang UniversitySeoulSouth Korea

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