MODIFIED KRASNOSELSKI-MANN ITERATIONS FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES
S. V. R. Naidu, Mengistu Goa Sangago · Journal of applied mathematics & informatics · 2010
Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K K be a contraction mapping. Let {} and {} be sequences in (0, 1) such that , (0.1) , (0.2) 0 b . (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {} given by {, , , , , (0.4) converges strongly to a point p Fix(T} which satisfies the variational inequality 0, z Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.