We consider general base i_α and j_β which perform the roles of i and j do in quaternions. We give a representation and properties of a Fourier transformation of regular functions with values in generalized quaternions, referring the Fourier transformation using quaternions.

In this paper, we study the existence of fixed points, demiclosedness principle and the structure of fixed point sets for the class of nearly asymptotically nonexpansive nonself-mappings in CAT(0) spaces, and also we discuss the strong and ∆-convergence theorems for an iterative scheme introduced by Khan. Our results are improvements of the various well-known results of fixed point theory which is established in uniformly convex Banach spaces as well as CAT(0) spaces.