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Nonlinear Analysis and Variational Problems pp 125–134Cite as

Fixed Points and Stability of Functional Equations

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 35))

Abstract

Using the fixed point method, we prove the generalized Hyers–Ulam stability of the functional equation \(f(x+y) + \frac{1}{2}f(x-y) + \frac{1}{2}f(y-x) = \frac{3}{2}f(x) + \frac{3}{2}f(y) +\frac{1}{2}f(-x) +\frac{1}{2} f(-y)\) in real Banach spaces.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hanyang University, 133-791, Seoul, South Korea

    Choonkil Park

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

    Themistocles M. Rassias

Authors
  1. Choonkil Park
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  2. Themistocles M. Rassias
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Corresponding author

Correspondence to Choonkil Park .

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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Park, C., Rassias, T.M. (2010). Fixed Points and Stability of Functional Equations. 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_11

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