Fixed point iteration for pseudocontractive maps

Let K be a compact convex subset of a real Hilbert space, H; T : K --> K a continuous pseudocontractive map. Let {a(n)}, {b(n)}, {c(n)}, {a'(n)}, {b'(n)} and{c'(n)} be real sequences in [0,1] satisfying appropriate conditions. For arbitrary x(1) is an element of K; define the sequence {x(n)}(n=1)(infinity) iteratively by x(n+1) = a(n)x(n) + b(n)Ty(n) + c(n)u(n); y(n) = a'(n)x(n) + b'(n)Tx(n) + c'(n)v(n); n greater than or equal to 1; where {u(n)}, {v(n)} are arbitrary sequences in K. Then, {x(n)}(n=1)(infinity) converges strongly to a fixed point of T. A related result deals with the convergence of {x(n)}(n=1)(infinity) to a fixed point of T when T is Lipschitz and pseudocontractive. Our theorems also hold for the slightly more general class of continuous hemicontractive nonlinear maps.