AIMS Mathematics, 2020, 5(3): 1693-1705. doi: 10.3934/math.2020114

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Solution of a 3-D cubic functional equation and its stability

1 Department of Mathematics, Sri Vidya Mandir Arts and Science College, Uthangarai, Tamil Nadu-636902, India
2 Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
3 Departmento de Cie ncias Exatas e Engenharia, Academia Militar, Portugal
4 Department of Mathematics, Sri Meenakshi GGHSS,Tirupattur, Tamil Nadu-635601, India

In this paper, we define and find the general solution of the following 3-D cubic functional equation\[\begin{array}{*{20}{c}}{f(2{x_1} + {x_2} + {x_3}) = 3({x_1} + {x_2} + {x_3}) + f( - {x_1} + {x_2} + {x_3}) + 2f({x_1} + {x_2}) + 2f({x_1} + {x_3})}\\{ - 6f({x_1} - {x_2}) - 6f({x_1} - {x_3}) - 3f({x_2} + {x_3}) + 2f({x_1} - {x_2})}\\{ + 2f(2{x_1} - {x_3}) - 18f({x_1}) - 6f({x_2}) - 6f({x_3})}\end{array}\]We also prove the Hyers-Ulam stability of this functional equation in fuzzy normed spaces by using the direct method and the fixed point method.
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