关键词: generalized Hyers-Ulam stability, Euler-Lagrange functional equation, non-Archimedean normed space, p-adic field

Abstract: In the last several years some progress has been made in the study of the properties of the extent of Banach space-.In 1979 for example, when Suillivan discussed a related characterization of real L^p(X) space, he used uniform behavior of all two-dimensional subspace and defined this concept of a KUR space.In 1980 Huff used the concept of a NUC space when he discussed the property of generalizing uniform convexity which was defined in terms of sequence. And in 1980 YuXin-tai stated certainly and proved that the KUR space is equal to the NUC space^[1] However, the following quite interesting questions raised respectively by Suillivan and Huff merit attention: Does every super-reflexive space have the fixed point property?^[2] The purpose of this paper is to study the characterization of transformation function^[4] and relationships between transformation function and the two questions above.

Key words: generalized Hyers-Ulam stability, Euler-Lagrange functional equation, non-Archimedean normed space, p-adic field