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

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

Abstract

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.

Keywords

Banach Space Functional Equation Additive Mapping Cauchy Sequence Logarithmic Function 
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Copyright information

© 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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