• Title/Summary/Keyword: generalized Hyers-Ulam stability

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ON THE STABILITY OF THE GENERALIZED G-TYPE FUNCTIONAL EQUATIONS

  • KIM, GWANG-HUI
    • Communications of the Korean Mathematical Society
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    • v.20 no.1
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    • pp.93-106
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    • 2005
  • In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.

A General Uniqueness Theorem concerning the Stability of AQCQ Type Functional Equations

  • Lee, Yang-Hi;Jung, Soon-Mo
    • Kyungpook Mathematical Journal
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    • v.58 no.2
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    • pp.291-305
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    • 2018
  • In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

HYERS-ULAM-RASSIAS STABILITY OF A CUBIC FUNCTIONAL EQUATION

  • Najati, Abbas
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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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.

GENERAL SOLUTION AND ULAM-HYERS STABILITY OF VIGINTI FUNCTIONAL EQUATIONS IN MULTI-BANACH SPACES

  • Murali, Ramdoss;Bodaghi, Abasalt;Raj, Aruldass Antony
    • Journal of the Chungcheong Mathematical Society
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    • v.31 no.2
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    • pp.199-230
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    • 2018
  • In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, we indicate an example for non-stability case regarding to this new functional equation.

ON THE GENERALIZED HYERS-ULAM STABILITY OF A BI-JENSEN FUNCTIONAL EQUATION

  • Jun, Kil-Woung;Lee, Ju-Ri;Lee, Yang-Hi
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.383-398
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    • 2009
  • In this paper, we study the generalized Hyers-Ulam stability of a bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,w)+f(y,\;z)+f(y,w)$$. Moreover, we establish stability results on the punctured domain.

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THE GENERALIZED HYERS-ULAM-RASSIAS STABILITY OF A CUBIC FUNCTIONAL EQUATION

  • Koh, Heejeong
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.2
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    • pp.165-174
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    • 2008
  • In this paper, we obtain the general solution, the generalized Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a cubic functional equation $4f(x+my)+4f(x-my)+m^2f(2x)=8f(x)+4m^2f(x+y)+4m^2f(x-y)$ for a positive integer $m{\geq}2$.

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