Strong convergence of new iterative algorithms for certain classes of asymptotically pseudocontractions
M. O. OSILIKE, P. U. Nwokoro, E. E. Chima · Fixed Point Theory and Applications · 2013
Let C be a nonempty closed convex subset of a real Hilbert space, and let be an asymptotically k-strictly pseudocontractive mapping with . Let and be real sequences in . Let be the sequence generated from an arbitrary by where is the metric projection. Under some appropriate mild conditions on and , we prove that converges strongly to a fixed point of T. Furthermore, if is uniformly L-Lipschitzian and asymptotically pseudocontractive with , we first prove that is demiclosed at 0, and then prove that under some suitable conditions on the real sequences , and in , the sequence generated from an arbitrary by converges strongly to a fixed point of T. No compactness assumption is imposed on T or C and no further requirement is imposed on . MSC:47H09, 47J25, 65J15.