and Applied Analysis 3 PK is called the metric projection ofH ontoK. It is well known that PK is a nonexpansive mapping ofH onto K and satisfies 〈x − y, PKx − PKy〉 ≥ ∥ PKx − PKy ∥ ∥ 2 , 2.3 for every x, y ∈ H. Moreover, PKx is characterized by the following properties: PKx ∈ K and 〈x − PKx, y − PKx〉 ≤ 0, ∥ ∥x − y∥∥ ≥ ‖x − PKx‖ ∥ ∥y − PKx ∥

1 In this paper, a modified Steffensen's type iterative scheme for the numerical solution of a system of nonlinear equations is studied. Two convergence theorems are presented. The numerical solution of boundary-value problems by the multiple shooting method using the proposed iterative scheme is analyzed. A unified approach for enlarging the radius of convergence for Newton's method and applic...

In this paper, we introduce and study a new iterative scheme toapproximate a common xed point for a nite family of generalized asymptoticallyquasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weakconvergence theorems of the proposed iteration are established. The main resultsobtained in this paper generalize and rene some known results in the currentliterature.

Variational inequalities are being used as a mathematical programming tool in modeling a wide class of problems arising in different branches of pure and applied sciences, see [1–26]. Variational inequalities have been extended and generalized in various directions using novel and innovative techniques. A useful and important generalization is called the general variational inclusion involving ...

Theobjective in this paper to study and present a new iterative method possessing high convergence order for calculating the polar decompostion of a matrix. To do this, it is shown that the new scheme is convergent and has high convergence. The analytical results are upheld via numerical simulations and comparisons.