AIMS Mathematics, 2020, 5(6): 7161-7174. doi: 10.3934/math.2020458

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Fuzzy normed spaces and stability of a generalized quadratic functional equation

1 Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
2 Department of Mathematics, Government Arts College for Men, Krishnagiri, Tamilnadu 635001, India
3 Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

In this paper, we acquire the general solution of the generalized quadratic functional equation \[ \begin{aligned} \sum_{1 \leq a < b < c \leq m}\varphi\left(r_{a}+r_{b}+r_{c}\right)&=(m-2)\sum_{1\leq a < b\leq m}\varphi\left(r_{a}+r_{b}\right) \\ &\quad-\left(\frac{m^{2}-3m+2}{2}\right)\nonumber \sum_{a=1}^{m}\frac{\varphi\left(r_{a}\right)+\varphi\left(-r_{a}\right)}{2} \end{aligned} \] 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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