Composite implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps

Let E be a real Banach space and let K be a nonempty closed convex subset of E. Let (T-i)(i=1)(N) be N strictly pseudocontractive self-maps of K such that F = boolean AND(N)(i=1) F(T-i) not equal 0, where F(T-i) {x is an element of K: T(i)x = x} and let {alpha(n)}(n=1)(infinity), {beta(n)}(n=1)(infinity) subset of[0, 1] be two real sequence satisfying the conditions: (i) Sigma(infinity)(n=1) (1 - alpha(n)) = + infinity; (ii) Sigma(infinity)(n=1) (1 - alpha(n))(2) < +infinity; (iii) Sigma(infinity)(n=1) (1 - beta(n)) < +infinity; (iv) (1 - alpha(n))(1 - beta(n))L-2 < 1, for all(n) >= 1, where L >= 1 is common Lipschitz constant of {T-i}(i=1)(N). For x(0) is an element of K, let {x(n)}(n=1)(infinity) be new implicit process defined by x(n) = alpha(n) x(n-1) + (1 - alpha(n)) T(n)y(n), y(n) = beta(n)x(n-1) +(1 - beta(n))T(n)x(n) where T-n = T-n mod N, then (i) lim(n-->infinity) parallel to x(n) - p parallel to exists, for all p is an element of F; (ii) lim inf(n-->infinity)parallel to x(n)-T(n)x(n)parallel to=0. The results of this paper generalize and improve the results of Osilike in 2004. In this paper, the proof methods of the main results are also different from that of Osilike. (C) 2005 Published by Elsevier Inc.