Abstract Let 1 ≤ m ≤ 4 be a fixed integer and let f : X → Y be a mapping with X , Y two real vector spaces. For any fixed integers a with a ≠ 0 , ± 1 , the following functional equation f ( a x + y ) + f ( a x − y ) = a m − 2 [ f ( x + y ) + f ( x − y ) ] + 2 ( a 2 − 1 ) [ a m − 2 f ( x ) + ( m − 2 ) ( 1 − ( m − 2 ) 2 ) 6 f ( y ) ] is said to be additive when m = 1 , quadratic when m = 2 , cubic when m = 3 and quartic when m = 4 , respectively. For convenience, a solution of the above functional equation will be called an m-mapping. In this paper, for each m = 1 , 2 , 3 , 4 , we apply the fixed point method to investigate Hyers-Ulam stability results concerning the above functional equation in quasi fuzzy p-normed spaces. We also discuss the fuzzy continuity behavior of fuzzy approximate m-mappings in quasi fuzzy p-normed spaces. As applications, we establish Hyers-Ulam stability results of approximate m-mappings from a linear space into a quasi p-normed space.

中文翻译：

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准模糊赋范空间中的模糊近似m-mappings

摘要 令 1 ≤ m ≤ 4 为一个固定整数，令 f : X → Y 为 X , Y 两个实向量空间的映射。对于任何具有 a ≠ 0 , ± 1 的固定整数 a，以下函数方程 f ( ax + y ) + f ( ax − y ) = am − 2 [ f ( x + y ) + f ( x − y ) ] + 2 ( a 2 − 1 ) [ am − 2 f ( x ) + ( m − 2 ) ( 1 − ( m − 2 ) 2 ) 6 f ( y ) ] 当 m = 1 时称为可加性，当 m 时称为二次= 2 ，当 m = 3 时为三次，当 m = 4 时分别为四次。为方便起见，上述函数方程的解将称为 m-mapping。在本文中，对于每个 m = 1 , 2 , 3 , 4 ，我们应用不动点方法来研究关于上述函数方程在准模糊 p 范数空间中的 Hyers-Ulam 稳定性结果。我们还讨论了准模糊 p 范数空间中模糊近似 m 映射的模糊连续性行为。作为应用程序，