Abstract :
Suppose that K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach
space E. Let T1,T2 :K →E be two nonself asymptotically nonexpansive mappings with sequences
{kn}, {ln} ⊂ [1,∞), limn→∞kn = 1, limn→∞ln = 1, F(T1) ∩ F(T2) = {x ∈ K: T1x = T2x = x} = ∅,
respectively. Suppose {xn} is generated iteratively by
x1 ∈ K,
xn+1 = P((1− αn)xn +αnT1(P T1)n−1yn),
yn = P((1−βn)xn +βnT2(P T2)n−1xn), n 1,
where {αn} and {βn} are two real sequences in [ , 1 − ] for some >0. (1) Strong convergence theorems
of {xn} to some q ∈ F(T1) ∩ F(T2) are obtained under conditions that one of T1 and T2 is completely
continuous or demicompact and ∞n=1(kn−1) <∞, ∞n=1(ln−1) <∞. (2) If E is real uniformly convex
Banach space satisfying Opial’s condition, then weak convergence of {xn} to some q ∈ F(T1) ∩ F(T2) is
obtained.
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