Strong convergence theorems for bounded accretive operators in uniformly smooth Banach spaces
C.E. Chidume · Contemporary mathematics - American Mathematical Society · 2016
Let E E be a uniformly smooth real Banach space and A : E → 2 E A:E\rightarrow 2^E be a multi-valued bounded m m -accretive mapping. Assume that the inclusion 0 ∈ A u 0\in Au has a solution. An iterative process is constructed which converges strongly to a solution of this inclusion. Our theorems complement several important results on the proximal point algorithm for approximating a solution of this inclusion (assuming existence). Furthermore, our theorems resolve some important open questions. We achieve this by combining our technique with a celebrated theorem of Reich on the strong convergence of the resolvent of m m -accretive operators in uniformly smooth real Banach spaces.