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On the Butler–Rassias Functional Equation and its Generalized Hyers–Ulam Stability

In: Functional Equations in Mathematical Analysis

Author

Listed:
  • Takeshi Miura

    (Yamagata University)

  • Go Hirasawa

    (Ibaraki University)

  • Takahiro Hayata

    (Yamagata University)

Abstract

In this paper, we present a recent development of the Hyers–Ulam stability of the Butler–Rassias functional equation $$f(x + y) - f(x)f(y) = d\sin x\sin y$$ . We also show our most recent results on a Butler–Rassias type functional equation with complex variables.

Suggested Citation

  • Takeshi Miura & Go Hirasawa & Takahiro Hayata, 2011. "On the Butler–Rassias Functional Equation and its Generalized Hyers–Ulam Stability," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 201-206, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_16
    DOI: 10.1007/978-1-4614-0055-4_16
    as

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