| Let C be a nonempty closed convex subset of a uniformly convex Banach space E whose norm is uniformly Gâteaux differentiable. Let {Tn } and T be families of nonexpansive mappings of C into itself such that Ø ≠ F (T ) ⊂ ∩n=1∞ F (Tn ), where F (Tn ) is the set of all fixed points of Tn and F (T ) is the set of all common fixed points of T . We consider a sequence {xn} generated by x ∈ C, xn = αn x + (1-αn )Tn xn (∀ n ∈ N ), where {αn } ⊂ (0,1) and then give the conditions of {αn }, {Tn } and T under which {xn} converges strongly to a common fixed point of T . We also consider a sequence {xn} generated by x 1=x ∈ C, x n+1= αn x + (1- αn )Tn (βn x + (1- βn) xn ) (∀ n ∈ N ), where αn ⊂ [0,1) and βn ⊂ [0,1) and then give the conditions of αn, βn, Tn and T under which {xn} converges strongly to a common fixed point of T. Using these results, we improve and extend well-known strong convergence theorems. |
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