Let q>1 and E be a real q-uniformly smooth Banach space, K be a nonempty closed convex subset of E and T:K→K be a Lipschitz continuous mapping. Let {un} and {vn } be bounded sequences in K and {αn} and {βn } be real sequences in [0,1] satisfying some restrictions. Let {xn} be the sequence generated from an arbitrary x1 K by the Ishikawa iteration process with errors: yn = (1-βn) xn +βn T xn + vn , xn+1= (1-αn) xn +αn Tyn + un , n≧1. Sufficient and necessary conditions for the strong convergence { xn } toa fixed point of T is established.
關聯:
International Conference of Analysis and Its Applications
