Strong convergence of approximated iterations for asymptotically pseudocontractive mappings

Strong convergence of approximated iterations for asymptotically pseudocontractive mappings

The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings. It is well known that the asymptotically nonexpansive mappings is a proper subclass of the class of asymptotically pseudocontractive mappings. In the present...

Strong Convergence for Semigroup of Asymptotically Pseudocontractive Mappings

In this paper, we propose a viscosity iteration process for semigroup of asymptotically pseudocontractive mappings, and prove a strong convergence theorem in uniformly convex Banach space for the proposed iteration process.

Strong convergence of two finite families of asymptotically pseudocontractive mappings

In this paper, we propose a modified implicit iteration for two finite families of asymptotically pseudocontractive mappings. Further, convergence theorems for approximation of common fixed points of two finite families of uniformly Lipschitzian asymptotically pseudocontractive mappings are proved in Banach spaces. Our results extend and improve a number of results in the literature. We also re...

Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings

Strong convergence of a CQmethod for k-strictly asymptotically pseudocontractive mappings

Let E be a real q-uniformly smooth Banach space, which is also uniformly convex (for example, Lp or p spaces, 1 < p <∞), and C be a nonempty bounded closed convex subset of E. Let T : C→ C be a k-strictly asymptotically pseudocontractive map with a nonempty fixed point set. A hybrid algorithm is constructed to approximate fixed points of such maps. Furthermore, strong convergence of the propose...