In the last two decades E. Pancheva and her collaborators were investigating various limit theorems for extremes using a wider class of normalizing mapping than the linear ones to get a wider class of limit laws. This wider class of extreme limits can be used in solving approximation problems. For extreme order statistics, in a recent paper by Sreehari (2009), the domains of attraction for general nonlinear normalizations are fully characterized, including the question of how to choose suitable norming functions from the knowledge of the sample distribution. The main aim of this thesis is...