Sharp Estimates of Homogeneous Expansion of almost Spirallike Mappings of Type β and Order α in B~n

The upper bounds of some items of homogeneous expansion for almost spirallike mappings of type β and order α on the unit ball in is studied from the point of view of Loewner chains,and as the special case,the upper bounds of some items of homogeneous expansion for spirallike mappings of type β,starlike mappings and almost starlike mappings of order α is obtained.The results extend the upper bounds of the second item of homogeneous expansion for spirallike mappings of type β and starlike mappings.