The Transformation Function Φ and the Condition Needed for KUR Space Having the Fixed Point

In the last several years some progress has been made in the study of the properties of the extent of Banaeh space: In 1979, for example, when SuiIIivan 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 an NUC space when he discussed the property of generalizing uniform convexity which was defined in terms of sequence; And in 1984 Yu Xin-tai(俞鑫泰)stated certainly and proved that the RKU space is equal to the NUC space^[1]. However, the following quite interesting questions raised by Suillivan and Huff merit attention; Does every super-reflexive space have the fixed point propertyyand what conditions are needed for an L^P(x) space to be NUC space^[3]? respectively. The purpose of this paper is to study the characterization of transformation functionary and relationships between transformation function ^[4] and the two questions above.