A GENERAL ITERATIVE ALGORITHM FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES

Let E be a real q-uniformly smooth Banach space whose duality map is weakly sequentially continuous. Let T : E -> E be a nonexpansive mapping with F(T) not equal (sic). Let A : E -> E be an eta-strongly accretive map which is also kappa-Lipschitzian. Let f : E -> E be a contraction map with coefficient 0 < alpha < 1. Let a sequence {y(n)} be defined iteratively by y(0) is an element of E, y(n+1) = alpha(n)gamma f(y(n)) + (I - alpha(n)mu A) Ty(n), n >= 0, where {alpha(n)}, gamma and mu satisfy some appropriate conditions. Then, we prove that {yn} converges strongly to the unique solution x* is an element of F(T) of the variational inequality <(gamma f - mu A)x*, j(y = x*)> <= 0, for all y is an element of F(T). Convergence of the correspondent implicit scheme is also proved without the assumption that E has weakly sequentially continuous duality map. Our results are applicable in l(p) spaces, 1 < p < infinity.