Convergence of the steepest descent method for accretive operators
Claudio H. Morales, C.E. Chidume · Proceedings of the American Mathematical Society · 1999
Let X X be a uniformly smooth Banach space and let A : X → X A\colon X\to X be a bounded demicontinuous mapping, which is also α \alpha -strongly accretive on X X . Let z ∈ X z\in X and let x 0 x_0 be an arbitrary initial value in X X . Then the approximating scheme \[ x n + 1 = x n − c n ( A x n − z ) , n = 0 , 1 , 2 , … , x_{n+1}=x_n-c_n(Ax_n-z),\qquad n=0,1,2,\dots , \] converges strongly to the unique solution of the equation A x = z Ax=z , provided that the sequence { c n } \{c_n\} fulfills suitable conditions.