• 제목/요약/키워드: stability functional equation

검색결과 415건 처리시간 0.023초

SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION

  • Lee, Young-Whan;Kim, Gwang-Hui;Lee, Jae-Ha
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제15권2호
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    • pp.169-178
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    • 2008
  • In this paper we generalize the superstability of the exponential functional equation proved by J. Baker et al. [2], that is, we solve an exponential type functional equation $$f(x+y)\;=\;a^{xy}f(x)f(y)$$ and obtain the superstability of this equation. Also we generalize the stability of the exponential type equation in the spirt of R. Ger[4] of the following setting $$|{\frac{f(x\;+\;y)}{{a^{xy}f(x)f(y)}}}\;-\;1|\;{\leq}\;{\delta}.$$

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STABILITY OF PEXIDERIZED JENSEN AND JENSEN TYPE FUNCTIONAL EQUATIONS ON RESTRICTED DOMAINS

  • Choi, Chang-Kwon
    • 대한수학회보
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    • 제56권3호
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    • pp.801-813
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    • 2019
  • In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation $$2f(\frac{x+y}{2})-g(x)-h(y)=0$$ and pexiderized Jensen type functional equations $$f(x+y)+g(x-y)-2h(x)=0,\\f(x+y)-g(x-y)-2h(y)=0$$ on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.

HYERS-ULAM-RASSIAS STABILITY OF A CUBIC FUNCTIONAL EQUATION

  • Najati, Abbas
    • 대한수학회보
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    • 제44권4호
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    • pp.825-840
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    • 2007
  • In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.