In 1970, Cesaro sequence spaces was introduced by Shiue. In 1981, Kızmaz defined difference sequence spaces for ℓ∞, c and c. Then, in 1983, Orhan introduced Cesa`ro Difference Sequence Spaces. Later, 0 Et and Tripathy et. al. generalized the space introduced by Orhan. Moreover, in 1989, C¸ olak obtained new types of sequence spaces by generalizing Kızmaz’s idea and using C¸ olak’s structure, Et and Esi, in 2000, obtained generalized difference sequences. Using Et and Esi’s structure, Ansari and Chaudhry, in 2012, introduced a new type of generalized difference sequence space. Et and Is¸ık, in 2012, obtained new type of generalized difference sequence spaces which have equivalent norm to that of Ansari and Chaudhry’s type Banach spaces. Then, Et and Is¸ık found α-duals of the Banach spaces they got and investigated geometric properties for them. In this study, firstly, we recall that in 1979, Goebel and Kuczomow showed that there exist large classes of closed bounded and convex subsets in ℓ1 with fixed point property for nonexpansive mappings. It is notable that after Goebel and Kuczumow’s study, Kaczor and Prus wanted to find large classes of closed bounded and convex subsets with fixed point property for asymptotically nonexpansive mappings; then indeed they gave positive answer in ℓ1. In this study, we study Kaczor and Prus analogy in the second and third order α-duals of difference sequence spaces introduced by Et and Is¸ık and show that affine asypmtotically nonexpansive mappings on large classes of closed, bounded and convex subsets of the Banach spaces taken have fixed points.