On a Weak Version of Hyers–Ulam Stability Theorem in Restricted Domains

Chapter
First Online:
Part of the Springer Optimization and Its Applications book series (SOIA, volume 96)

Abstract

In this chapter we consider a weak version of the Hyers–Ulam stability problem for the Pexider equation, Cauchy equation satisfied in restricted domains in a group when the target space of the functions is a 2-divisible commutative group. As the main result we find an approximate sequence for the unknown function satisfying the Pexider functional inequality, the limit of which is the approximate function in the Hyers–Ulam stability theorem.

Keywords

Hyers–Ulam stability Functional equations Restricted domains Pexider equation 2-divisible commutative group 
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Notes

Acknowledgements

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST) (no. 2012008507).

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Copyright information

© Springer Science+Business Media, LLC 2014

Authors and Affiliations

  1. 1.Department of MathematicsKunsan National UniversityKunsanRepublic of Korea
  2. 2.Department of Mathematics EducationDankook UniversityYonginRepublic of Korea

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