In this paper, we will investigate the Hyers-Ulam stability of the following functional equations and where is a compact subgroup of morphisms of , is a normalized Haar measure of , is a complex -invariant measure with compact support, the functions are continuous on and is assumed to satisfies the Kannappan type condition The paper of Székelyhidi [30] is the essential motivation for the present work and the methods used here are closely related to and inspired by those in [30]. The concept of the generalized Hyers-Ulam stability of mappings was introduced in the subject of functional equations by Th. M. Rassias in [20].
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机译：在本文中，我们将研究以下函数方程的Hyers-Ulam稳定性，其中，是的一个紧凑的态素子群，是的规范化Haar度量，是具有紧支撑的复不变性度量，函数在和上是连续的Székelyhidi[30]的论文是目前工作的主要动力，本文使用的方法与[30]中的方法紧密相关，并受其启发，被认为可以满足Kannappan型条件。 Th在函数方程的主题中引入了映射的广义Hyers-Ulam稳定性的概念。 M. Rassias在[20]中。
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