• 제목/요약/키워드: Exponential functional equation

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SUPERSTABILITY OF A GENERALIZED EXPONENTIAL FUNCTIONAL EQUATION OF PEXIDER TYPE

  • Lee, Young-Whan
    • 대한수학회논문집
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    • 제23권3호
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    • pp.357-369
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    • 2008
  • We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

APPROXIMATE PEXIDERIZED EXPONENTIAL TYPE FUNCTIONS

  • Lee, Young-Whan
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제19권2호
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    • pp.193-198
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    • 2012
  • We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

APPROXIMATE GENERALIZED EXPONENTIAL FUNCTIONS

  • Lee, Eun-Hwi
    • 호남수학학술지
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    • 제31권3호
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    • pp.451-462
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    • 2009
  • In this paper we prove the superstability of a generalized exponential functional equation $f(x+y)=a^{2xy-1}g(x)f(y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker. Also we investigate the stability of this functional equation in the following form : ${\frac{1}{1+{\delta}}}{\leq}{\frac{f(x+y)}{a^{2xy-1}g(x)f(y)}}{\leq}1+{\delta}$.

STABILITY OF PARTIALLY PEXIDERIZED EXPONENTIAL-RADICAL FUNCTIONAL EQUATION

  • Choi, Chang-Kwon
    • 대한수학회보
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    • 제58권2호
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    • pp.269-275
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    • 2021
  • Let ℝ be the set of real numbers, f, g : ℝ → ℝ and �� ≥ 0. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation $$f({\sqrt[n]{x^N+y^N}})=f(x)g(y)$$ for all x, y ∈ ℝ, i.e., we investigate the functional inequality $$\|f({\sqrt[n]{x^N+y^N}})-f(x)g(y)\|{\leq}{\epsilon}$$ for all x, y ∈ ℝ.

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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THE STABILITY OF K-EXPONENTIAL EQUATIONS

  • Lee, Young-Whan
    • Journal of applied mathematics & informatics
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    • 제6권3호
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    • pp.929-935
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    • 1999
  • By applications of the stability for a class of functional equa-tions we obtain the hyers-Ulam stability for the equations of the form g($\chi$+y)=kg($\chi$)g(y) in the following setting; |g($\chi$+y)-kg($\chi$)g(y)|$\leq$$\Delta$($\chi$,y).

LOCAL EXISTENCE AND EXPONENTIAL DECAY OF SOLUTIONS FOR A NONLINEAR PSEUDOPARABOLIC EQUATION WITH VISCOELASTIC TERM

  • Nhan, Nguyen Huu;Nhan, Truong Thi;Ngoc, Le Thi Phuong;Long, Nguyen Thanh
    • Nonlinear Functional Analysis and Applications
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    • 제26권1호
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    • pp.35-64
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    • 2021
  • In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.

ON THE SUPERSTABILITY OF SOME PEXIDER TYPE FUNCTIONAL EQUATION II

  • Kim, Gwang-Hui
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제17권4호
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    • pp.397-411
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    • 2010
  • In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.