STRONG CONVERGENCE TO ZEROS OF ACCRETIVE OPERATORS IN BANACH SPACES

Let C be a nonempty closed convex subset of a uniformly convex Banach space E whose norm is uniformly Gateaux differentiable and let A subset of E x E be an accretive operator such that A(-1)0 not equal empty set and <(D(A))over bar> subset of C subset of boolean AND R-lambda>0(I+lambda A). Then, we consider a sequence {x(n)} generated by x is an element of C, x(n) = alpha(n)x + (1 - alpha(n))J(lambda n)x(n) (for all n is an element of N), where {alpha(n)} subset of (0,1), {lambda(n)} subset of (0, infinity) and J(lambda n) is the resolvent of A and prove that if lim(n ->infinity) alpha(n) = lim(n ->infinity) alpha(n)/lambda(n) = 0, {x(n)} converges strongly to some element of A(-1)0. And we consider a sequence {x(n)} generated by x(1) = x is an element of C, x(n+1) = alpha(n)x + (1 - alpha(n))J(lambda n)x(n) (for all n is an element of N), where {alpha(n)} subset of [0,1] and {lambda(n)} subset of (0, infinity) and proved that if lim(n ->infinity) alpha(n) = 0, Sigma(infinity)(n=1) alpha(n) = infinity, Sigma(infinity)(n=1) vertical bar alpha(n)-alpha(n+1)vertical bar < infinity, lim inf(n ->infinity) lambda(n) > 0 and Sigma(infinity)(n=1) vertical bar lambda(n) - lambda(n+1)vertical bar < infinity, {x(n)} converges strongly to some element of A(-1)0.