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

In: Nonlinear Analysis and Variational Problems

Author

Listed:
  • Soon-Mo Jung

    (Mathematics Section, College of Science and Technology, Hongik University)

  • Themistocles M. Rassias

    (National Technical University of Athens, Zografou Campus)

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.

Suggested Citation

  • Soon-Mo Jung & Themistocles M. Rassias, 2010. "A Fixed Point Approach to the Stability of a Logarithmic Functional Equation," Springer Optimization and Its Applications, in: Panos M. Pardalos & Themistocles M. Rassias & Akhtar A. Khan (ed.), Nonlinear Analysis and Variational Problems, chapter 0, pages 99-109, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-0158-3_9
    DOI: 10.1007/978-1-4419-0158-3_9
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    Cited by:

    1. Kui Liu & Michal Fečkan & JinRong Wang, 2020. "A Fixed-Point Approach to the Hyers–Ulam Stability of Caputo–Fabrizio Fractional Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    2. Masoumeh Madadi & Reza Saadati & Manuel De la Sen, 2020. "Stability of Unbounded Differential Equations in Menger k -Normed Spaces: A Fixed Point Technique," Mathematics, MDPI, vol. 8(3), pages 1-10, March.

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