Iterative Approximation of Common Fixed Points of Two Nonself Asymptotically Nonexpansive Mappings
Esref Turkmen, Safeer Hussain Khan, Murat Özdemir · Discrete Dynamics in Nature and Society · 2011
Suppose that K is nonempty closed convex subset of a uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction and F : = F ( T 1 )∩ F ( T 2 ) = { x ∈ K : T 1 x = T 2 x = x } ≠ ∅ . Let T 1 , T 2 : K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with two sequences satisfying ( i = 1,2), respectively. For any given x 1 ∈ K , suppose that { x n } is a sequence generated iteratively by , , n ∈ ℕ , where { α n } and { β n } are sequences in [ a , 1 − a ] for some a ∈ (0,1). Under some suitable conditions, the strong and weak convergence theorems of { x n } to a common fixed point of T 1 and T 2 are obtained.