Iterative Approximation with Errors of Fixed Point for a Class of Nonlinear Operation with a Bounder Range

Let X be a uniformly smooth real Banach space. Let T:X→X be a continuous and strongly accretive operator. For a given ∀f∈X,define S:X_x→X,for all ∀x∈X,Let {α_n}_n^∞=0 be two real sequences in(0,1) satisfying:(ⅰ)α_n→0,β_n→0(n→∞);.Assume that {u_n}_n^∞=0 and {v_n}_n^∞=0 are two sequences in X satisfying ‖un‖= o (A_n) and ‖v_n‖→0 as n→∞].For arbitrary x₀∈X, the iteration sequence {x_n} is defined by Moreover, suppose that {S_nx_n} and {Sy_n} are bounded, then {x_n} converges strongly to the unique fixed point of S.