In this paper, I introduce an implicit iterative process with mixed errors for two finite family of total asymptotically nonexpansive mappings in a uniformly convex Banach space and prove strong convergence theorems under some conditions. My results improved and extended many know results existing in the literature.

In this paper, under the framework of Banach space with uniformly Gateaux differentiable norm and uniform normal structure, we use the existence theorem of fixed points of Li and Sims to investigate the convergence of the implicit iteration process and the explicit iteration process for asymptotically nonexpansive mappings. We get the convergence theorems.

In this paper, under the framework of Banach space with uniformly Gateauxdifferentiable norm and uniform normal structure, we use the existence theorem of fixed points of Gang Li and Sims to investigate the convergence of the implicit iteration process and the explicit iteration process for asymptotically nonexpansive semigroup. We get the convergence theorems.

In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767–77...

Suppose C is a nonempty closed convex subset of real Hilbert space H . Let T : C → H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn = (1−αn)u+αnT[(1− βn)xn + βnTxn], yn = (1−αn)u+αnPT[(1− βn)yn + βnPTyn], and zn = P[(1 − αn)u + αnTP[(1 − βn)zn + βnTzn]], where {αn} ⊆ (0...

A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has ...