• Title/Summary/Keyword: generalized quadratic mappings

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APPROXIMATION OF ALMOST EULER-LAGRANGE QUADRATIC MAPPINGS BY QUADRATIC MAPPINGS

  • John Michael Rassias;Hark-Mahn Kim;Eunyoung Son
    • Journal of the Chungcheong Mathematical Society
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    • v.37 no.2
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    • pp.87-97
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    • 2024
  • For any fixed integers k, l with kl(l - 1) ≠ 0, we establish the generalized Hyers-Ulam stability of an Euler-Lagrange quadratic functional equation f(kx + ly) + f(kx - ly) + 2(l - 1)[k2f(x) - lf(y)] = l[f(kx + y) + f(kx - y)] in normed spaces and in non-Archimedean spaces, respectively.

GENERALIZED STABILITY OF EULER-LAGRANGE TYPE QUADRATIC MAPPINGS

  • Jun, Kil-Woung;Oh, Jeong-Ha
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.535-542
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    • 2007
  • In this paper, we investigate the generalized Hyers-Ulam{Rasssias stability of the following Euler-Lagrange type quadratic functional equation $$f(ax+by+cz)+f(ax+by-cz)+f(ax-by+cz)+f(ax-by-cz)=4a^2f(x)+4b^2f(y)+4c^2f(z)$$.

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FUZZY STABILITY OF QUADRATIC-CUBIC FUNCTIONAL EQUATIONS

  • Kim, Chang Il;Yun, Yong Sik
    • East Asian mathematical journal
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    • v.32 no.3
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    • pp.413-423
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    • 2016
  • In this paper, we consider the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy Banach space. The usual method to obtain the stability for mixed type functional equation is to split the cases according to whether the involving mappings are odd or even. In this paper, we show that the stability of a quadratic-cubic mapping can be obtained without distinguishing the two cases.

SOLUTION AND STABILITY OF MIXED TYPE FUNCTIONAL EQUATIONS

  • Jun, Kil-Woung;Jung, Il-Sook;Kim, Hark-Mahn
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.4
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    • pp.815-830
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    • 2009
  • In this paper we establish the general solution of the following functional equation with mixed type of quadratic and additive mappings f(mx+y)+f(mx-y)+2f(x)=f(x+y)+f(x-y)+2f(mx), where $m{\geq}2$ is a positive integer, and then investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.

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