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Acta Mathematica Hungarica

, Volume 159, Issue 2, pp 358–373 | Cite as

On stability and hyperstability of additive equations on a commutative semigroup

  • S. SaejungEmail author
  • J. Senasukh
Article
  • 31 Downloads

Abstract

We prove the stability and hyperstability results for the additive functional equations on restricted domains (subsets of a commutative semigroup). The proof is based on the modified Brzdęk's fixed point theorem. Next, we introduce the concepts of modulus-additive and approximately modulus-additive functions and deduce, from our main theorem, some stability and hyperstability outcomes for the modulus-additive equation. We also obtain some results for the radical quadratic functional equation. Finally, we point out some faulty assumptions in a result of Aiemsomboon and Sintunavarat [1].

Key words and phrases

hyperstability stability modulus-additive function radical quadratic function 

Mathematics Subject Classification

primary 39B82 secondary 47H10 

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Notes

Acknowledgement

The authors thank the referee for their valuable suggestions and comments which enhance the presentation of the paper.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKhon Kaen UniversityKhon KaenThailand
  2. 2.Research Center for Environmental and Hazardous Substance ManagementKhon Kaen UniversityKhon KaenThailand

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