A Fixed Point Approach to the Stability of a Logarithmic Functional Equation

  • Soon-Mo Jung
  • Themistocles M. Rassias
Part of the Springer Optimization and Its Applications book series (SOIA, volume 35)


We will apply the fixed point method for proving the Hyers–Ulam–Rassias stability of a logarithmic functional equation of the form \(f(\sqrt{xy}) = \frac{1}{2} f(x) + \frac{1}{2} f(y),\) where f: (0,∞) → E is a given function and E is a real (or complex) vector space.


Banach Space Functional Equation Additive Mapping Cauchy Sequence Logarithmic Function 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematics Section, College of Science and Technology, Hongik UniversityJochiwonRepublic of Korea
  2. 2.Department of MathematicsNational Technical University of Athens, Zografou CampusAthensGreece

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