本文的目的是研究Cauchy函数方程的Ulam问题。首先，我们给出了关于交换半群上的类函数的柯西指数函数方程及其Pexiderized到酉复巴拿赫代数的超稳定性和稳定性的一些新结果。关于Th. M. Rassias和我们的结果，推广了Baker定理和L. Sze'kelyhidi。在适当的条件下，证明了交换半群上Cauchy可加函数方程的超稳定性。应用这个结果研究了对数函数方程的一个超稳定性结果，并对第31届ISFE中的问题18给出了部分肯定的回答.在适当的条件下，研究了交换半群上的函数到复赋范线性空间的Cauchy可加函数方程及其Pexiderized化的超稳定性和渐近性.作为我们结果的一些结果，我们给出了斯考夫定理S.-的一些推广M. Jesus定理，和另一个肯定的答案问题18，在第31 ISFE。并结合G。L.此外，在第13届ICFEI（2009）中，我们考虑了一些齐次线性方程组，我们的目标是建立这些函数方程系统的一些共同的Hyers-Ulam-Rassias稳定性，并给出这些结果的一些应用。
英文摘要：
Our aim is to study the Ulam's problem for Cauchy's functional equations. First, we present some new results about the superstability and stability of Cauchy exponential functional equation and its Pexiderized for class functions on commutative semigroup to unitary complex Banach algebra. In connection with the problem of Th. M. Rassias and our results, we generalize the theorem of Baker and theorem of L. Sze'kelyhidi. Then the superstability of Cauchy additive functional equation can be prove for complex valued functions on commutative semigroup under some suitable conditions. This result is applied to the study of a superstability result for the logarithmic functional equation, and to give a partial affirmative answer to problem 18, in the thirty-first ISFE. The hyperstability and asymptotic behaviors of Cauchy additive functional equation and its Pexiderized can be study for functions on commutative semigroup to a complex normed linear space under some suitable conditions. As some consequences of our results, we give some generalizations of Skof's theorem, S.-M. Joung's theorem, and another affirmative answer to problem 18, in the thirty-first ISFE. Also we study the stability of Cauchy linear equation in general form and in connection with the problem of G. L. Forti, in the 13th ICFEI (2009), we consider some systems of homogeneous linear equations and our aim is to establish some common Hyers-Ulam-Rassias stability for these systems of functional equations and presenting some applications of these results.
