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

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Nonlinear Analysis and Variational Problems

Part of the book series: Springer Optimization and Its Applications ((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.

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Author information

Authors and Affiliations

  1. Mathematics Section, College of Science and Technology, Hongik University, 339-701, Jochiwon, Republic of Korea

    Soon-Mo Jung

  2. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Themistocles M. Rassias

Authors
  1. Soon-Mo Jung
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  2. Themistocles M. Rassias
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Corresponding author

Correspondence to Soon-Mo Jung .

Editor information

Editors and Affiliations

  1. Dept. Industrial & Systems, Engineering, University of Florida, Weil Hall 303, Gainesville, 32611-6595, Florida, USA

    Panos M. Pardalos

  2. Zagoras Street 4, Athens, 151 25, Greece

    Themistocles M. Rassias

  3. School of Mathematical Sciences, Rochester Institute of Technology, Lomb Memorial Drive 85, Rochester, 14623-5602, USA

    Akhtar A. Khan

Additional information

Dedicated to the memory of Professor George Isac

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Jung, SM., Rassias, T.M. (2010). A Fixed Point Approach to the Stability of a Logarithmic Functional Equation. In: Pardalos, P., Rassias, T., Khan, A. (eds) Nonlinear Analysis and Variational Problems. Springer Optimization and Its Applications, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0158-3_9

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