• Title, Summary, Keyword: functional equations

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GENERALIZED FORMS OF SWIATAK'S FUNCTIONAL EQUATIONS WITH INVOLUTION

  • Wang, Zhihua
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.779-787
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    • 2019
  • In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.

ON A CLASS OF GENERALIZED LOGARITHMIC FUNCTIONAL EQUATIONS

  • Chung, Jae-Young
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.325-332
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    • 2009
  • Reducing the generalized logarithmic functional equations to differential equations in the sense of Schwartz distributions, we find the locally integrable solutions of the equations.

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THE INSTABILITY FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Ko, Young-Hee
    • Journal of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.757-771
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    • 1999
  • We consider a system of functional differential equations x'(t)=F(t, $x_t$) and obtain conditions on a Liapunov functional and a Liapunov function to ensure the instability of the zero solution.

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A General System of Nonlinear Functional Equations in Non-Archimedean Spaces

  • Ghaemi, Mohammad Bagher;Majani, Hamid;Gordji, Madjid Eshaghi
    • Kyungpook Mathematical Journal
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    • v.53 no.3
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    • pp.419-433
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    • 2013
  • In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.

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

  • Choi, Chang-Kwon
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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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.