Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space

Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space

A extension of Nakajo and Takahashi’s modification of Mann’s iterative process to the Ishikawa iterative process is given. The strong convergence of a modified Ishikawa iterative scheme to a common fixed point of a finite family of Lipschitz pseudocontractive self-mappings on a closed convex subset of a Hilbert space is proved. Our theorem extends several known results. c © 2007 Elsevier Ltd. A...

Strong convergence of shrinking projection methods for a family of pseudocontractive mappings in Hilbert spaces

The shrinking projection method has gained more and more attention as a powerful tool for the approximation of a fixed point of nonlinear mappings. In this paper, we introduce a new shrinking projection method for the approximation of fixed points of a family of pseudocontractive mappings in a Hilbert space. Using this method, we also deal with the problem of finding a common zero of a family o...

On Convergence Results for Lipschitz Pseudocontractive Mappings

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

A Weak Convergence Theorem for Total Asymptotically Pseudocontractive Mappings in Hilbert Spaces

Throughout this paper, we always assume thatH is a real Hilbert space, whose inner product and norm are denoted by 〈·, ·〉 and ‖ · ‖. → and ⇀ are denoted by strong convergence and weak convergence, respectively. Let C be a nonempty closed convex subset ofH and T : C → C a mapping. In this paper, we denote the fixed point set of T by F T . T is said to be a contraction if there exists a constant ...