Research article

Fuzzy normed spaces and stability of a generalized quadratic functional equation

  • Received: 10 June 2020 Accepted: 02 September 2020 Published: 10 September 2020
  • MSC : 46S40, 39B52, 39B82, 26E50, 46S50

  • In this paper, we acquire the general solution of the generalized quadratic functional equation $ \begin{aligned} \sum\limits_{1 \leq a \lt b \lt c \leq m}\varphi\left(r_{a}+r_{b}+r_{c}\right)& = (m-2)\sum\limits_{1\leq a \lt b\leq m}\varphi\left(r_{a}+r_{b}\right) \\ &\quad-\left(\frac{m^{2}-3m+2}{2}\right)\nonumber \sum\limits_{a = 1}^{m}\frac{\varphi\left(r_{a}\right)+\varphi\left(-r_{a}\right)}{2} \end{aligned} $ where $m\geqslant 3$ is an integer. We also investigate Hyers-Ulam stability results by means of using alternative fixed point theorem for this generalized quadratic functional equation.

    Citation: Choonkil Park, K. Tamilvanan, Batool Noori, M. B. Moghimi, Abbas Najati. Fuzzy normed spaces and stability of a generalized quadratic functional equation[J]. AIMS Mathematics, 2020, 5(6): 7161-7174. doi: 10.3934/math.2020458

    Related Papers:

  • In this paper, we acquire the general solution of the generalized quadratic functional equation $ \begin{aligned} \sum\limits_{1 \leq a \lt b \lt c \leq m}\varphi\left(r_{a}+r_{b}+r_{c}\right)& = (m-2)\sum\limits_{1\leq a \lt b\leq m}\varphi\left(r_{a}+r_{b}\right) \\ &\quad-\left(\frac{m^{2}-3m+2}{2}\right)\nonumber \sum\limits_{a = 1}^{m}\frac{\varphi\left(r_{a}\right)+\varphi\left(-r_{a}\right)}{2} \end{aligned} $ where $m\geqslant 3$ is an integer. We also investigate Hyers-Ulam stability results by means of using alternative fixed point theorem for this generalized quadratic functional equation.


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