Journal of Global Optimization

, Volume 59, Issue 1, pp 165–171 | Cite as

On the stability of the linear functional equation in a single variable on complete metric groups

  • Soon-Mo Jung
  • Dorian Popa
  • Michael Th. Rassias


In this paper we obtain a result on Hyers–Ulam stability of the linear functional equation in a single variable \(f(\varphi (x)) = g(x) \cdot f(x)\) on a complete metric group.


Optimization Stability Functional equation Complete metric group Inequalities Banach spaces Operator mapping Euler–Mascheroni constant 

Mathematics Subject Classification

33B15 11B34 41A30 39B22 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Soon-Mo Jung
    • 1
  • Dorian Popa
    • 2
  • Michael Th. Rassias
    • 3
  1. 1.Mathematics Section, College of Science and TechnologyHongik UniversitySejongRepublic of Korea
  2. 2.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania
  3. 3.Department of MathematicsETH-ZürichZurichSwitzerland

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