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 x
₀
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.