Journal of Global Optimization

, Volume 59, Issue 1, pp 165–171

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

Article

DOI: 10.1007/s10898-013-0083-9

Cite this article as:
Jung, S., Popa, D. & Rassias, M.T. J Glob Optim (2014) 59: 165. doi:10.1007/s10898-013-0083-9

Abstract

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.

Keywords

OptimizationStabilityFunctional equationComplete metric groupInequalitiesBanach spacesOperator mappingEuler–Mascheroni constant

Mathematics Subject Classification

33B1511B3441A3039B22

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