Geodesic
Convergence theorems for a finite family of nonexpansive and asymptotically nonexpansive mappings
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 139-152.

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In this paper, weak and strong convergence of finite step iteration sequences to a common fixed point for a pair of a finite family of nonexpansive mappings and a finite family of asymptotically nonexpansive mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented.
Classification : 47H09, 47H10, 47J25
Keywords: Nonexpansive mapping; asymptotically nonexpansive mapping; common fixed point; finite-step iterative sequence 
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Sitthikul, Kittipong; Saejung, Satit. Convergence theorems for a finite family of nonexpansive and asymptotically nonexpansive mappings. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 139-152. http://geodesic.mathdoc.fr/item/AUPO_2009__48_1_a11/