Let H be a Hilbert space and C a nonempty closed convex subset of H. Let A : C → H be a maximal monotone mapping and f : C → C a bounded demicontinuous strong pseudocontraction. Let {xt} be the unique solution to the equation f x x tAx. Then{xt} is bounded if and only if {xt} converges strongly to a zero point of A as t → ∞ which is the unique solution in A−1 0 , where A−1 0 denotes the zero se...

with respect to the Euclidian norm, where F :Rn →Rn is a nonlinear operator. Section 2 is devoted to a brief description of asynchronous parallel algorithm. In Section 3, we prove the main result concerning the convergence of the general algorithm in the synchronous case to a fixed point of a nonlinear operator fromRn to Rn. A particular case of this algorithm (algorithm of Jacobi) is applied i...

Inspired by the very recent work by Noor and Noor [9] and given a closed convex set-valued mapping C, we propose a split algorithm for solving the problem of finding an element x∗ which is a zero of a given maximal monotone operator T such that its image, Ax∗, under a linear operator, A, is in a closed convex set C(x∗). Then, we present two strong convergence results and state some examples as ...