The purpose of this paper is to study the weak and strong convergence of an implicit iteration process to a common fixed point for a finite family of nonexpansive nonself-mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [Xu and Ori, Numer. Funct. Anal. optim. 22(2001) 767-773; Zhou and Chang, Numer. Fund. Anal. Optim. 23(2002) 911-92...

Combining these three definitions, Zamfirescu [12] proved the following important result. Theorem 1.1. Let (X ,d) be a complete metric space and T : X → X a mapping for which there exists the real numbers a,b, and c satisfying a∈ (0,1), b,c ∈ (0,1/2) such that for each pair x, y ∈ X , at least one of the following conditions holds: (z1) d(Tx,Ty)≤ ad(x, y), (z2) d(Tx,Ty)≤ b[d(x,Tx) +d(y,Ty)], (z...

PSIDE is a code for solving implicit differential equations on parallel computers. It is an implementation of the four-stage Radau IIA method. The nonlinear systems are solved by a modified Newton process, in which every Newton iterate itself is computed by an iteration process. This process is constructed such that the four stage values can be computed simultaneously. We describe here how PSID...

In this paper, first we use an example to show the efficiency of $M$ iteration process introduced by Ullah and Arshad [4] for approximating fixed points of Suzuki generalized nonexpansive mappings. Then by using $M$ iteration process, we prove some strong and $Delta -$convergence theorems for Suzuki generalized nonexpansive mappings in the setting of $CAT(0)$ Spaces. Our results are the extensi...

A MULTI-STEP IMPLICIT ITERATIVE PROCESS FOR COMMON FIXED POINTS OF GENERALIZED C-OPERATORS IN CONVEX METRIC SPACES Zahid Akhtar, Hafiz Fukhar-ud-din, Ali Ahmad and Muhammad Ibrahim 1 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan. College of computer Science and information systems, Jazan University, Jazan, Saudi Arabia. Center for Advanced Studies ...

The implementation of implicit Runge{Kutta methods requires the solution of large systems of non-linear equations. Normally these equations are solved by a modiied Newton process, which can be very expensive for problems of high dimension. The recently proposed triangularly implicit iteration methods for ODE-IVP solvers 5] substitute the Runge{Kutta matrix A in the Newton process for a triangul...

A new version of the alternating directions implicit (ADI) iteration for the solution of large-scale Lyapunov equations is introduced. It generalizes the hitherto existing iteration, by incorporating tangential directions in the way they are already available for rational Krylov subspaces. Additionally, first strategies to adaptively select shifts and tangential directions in each iteration are...