Global convergence theorems of regularization iterative algorithm in uniformly smooth Banach spaces

Let E be a real uniformly smooth Banach space and A : D(A) sube E rarr 2^E be a m-accretive mapping which satisfies a linear growth condition of the form ||u|| les C (1 + ||x||) for some constant C > 0 and for all x isin E and u isin Ax, z isin D(A) be an arbitrary element. Suppose A^-1 0 ne oslash. The sequence {x_n} sub D(A) is generated from arbitrary x₀ isin D (A) by x_n+l isin x_n -lambda_n (u_n + thetas_n (x_n - z)), u_n isin Ax_n, n ges 0, where {lambda_n} and {thetas_n{ are acceptably paired, then {x_n{ converges strongly to x* isin A^-(0). As its application, we have deduced a strong convergence theorem for the iterative algorithm of fixed points for continuous pseudocontractions.