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Fuzzy Stability of an Additive-Quartic Functional Equation: A Fixed Point Approach

In: Functional Equations in Mathematical Analysis

Author

Listed:
  • Choonkil Park

    (Hanyang University)

  • Themistocles M. Rassias

    (National Technical University of Athens)

Abstract

Mirmostafaee, Mirzavaziri and Moslehian have investigated the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces. Using the fixed point method, we prove the generalized Hyers–Ulam stability of the following additive-quartic functional equation $$\begin{array}{rcl} f(2x + y) + f(2x - y) =& & 2f(x + y) + 2f(-x - y) + 2f(x - y) + 2f(y - x) \\ & & +14f(x) + 10f(-x) - 3f(y) - 3f(-y) \\ \end{array}$$ in fuzzy Banach spaces.

Suggested Citation

  • Choonkil Park & Themistocles M. Rassias, 2011. "Fuzzy Stability of an Additive-Quartic Functional Equation: A Fixed Point Approach," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 247-260, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_20
    DOI: 10.1007/978-1-4614-0055-4_20
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