Chiang Mai Journal of Science

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Suppose that  K  is a nonempty closed convex subset of  a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T , S : K → E  be two nonexpansive non-self maps, with F(T) ∩ F(S) :={x ∈K : Sx =Tx= x}  ≠∅  . Suppose {X_n} is generated iteratively by 

X_n+1 = P((1-α_nSP[(1-β_n)X_n + β_nTx_n]),X₁ ∈ K ,  n ≥ 1,

where {α_n} and {β_n} are real sequences in [ε, 1-ε ]  for some ε ∈(0,1) . It is proved that

(a) If   the dual E^* of   E has the Kadec-Klee property, then {X_n} weak convergesto some x^* ∈ F(T) ∩ F(S).
(b) If  T and  S satisfies condition (A), then {X_n} strong converges to some X^* ∈ F(T) ∩ F(S)

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