ABSTRACT S. M. Ulam once addressed the problem ‘when is it true that a mathematical object satisfying a certain property approximately must be close to an object satisfying the property exactly?’. This problem was solved by D. H. Hyers in 1941 using the functional equation and thereafter numerous research papers and monographs have been published for various types of functional equations in different spaces. The solution proposed by D. H. Hyers (1941) later developed into the famous generalized Hyers-Ulam-Rassias stability of functional equations. In this paper, we intend to attain the general solution to a new mixed type functional equation and interrogate the generalized Hyers–Ulam–Rassias stability in fuzzy normed spaces. Also, we seek to provide its application for generating secret keys in client–server environment.

中文翻译：

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基于模糊概念的赋范空间混合型泛函方程的稳定性

摘要 SM Ulam 曾经解决过“什么时候满足某个性质的数学对象必须接近于恰好满足该性质的对象？”的问题。DH Hyers 在 1941 年使用泛函方程解决了这个问题，此后针对不同空间中的各种类型的泛函方程发表了大量研究论文和专着。DH Hyers (1941) 提出的解后来发展成为著名的广义泛函方程的Hyers-Ulam-Rassias稳定性。在本文中，我们打算获得一个新的混合型泛函方程的一般解，并在模糊赋范空间中询问广义的 Hyers-Ulam-Rassias 稳定性。此外，我们寻求提供其在客户端 - 服务器环境中生成密钥的应用程序。