For an asymptotically non-expansive self-mapping T, we will prove the strong convergence of {xn} defined by xn+1 = (1−an−bn)xn+anu+bnTnxn, xn+1 = anu+(1−an)Tnxn, whenever {bn}, {an}Ì (0,1) satisfy (C1) limn®¥ an=0, (C2) S¥n=0 =¥ (C3) limn®¥ Kn-1/an = 0 or (C4) S¥n=0 (kn-1)<+¥ application, we also establish the strong convergence of the viscosity approximation schemes with a contraction ¦ given by xn+1 = anf (xn) + (1 −an)Tnxn and xn+1 = (1 −an− bn)xn+an f(xn) +bnTnxn.

In [1], introduce a modified variational iteration method (MVIM) for a special kind of nonlinear differential equations. In this paper, we consider variational iteration method (VIM) and MVIM (introduced in [1]) to obtain exact solution to Fisher’s equation. It is shown in this paper the application of VIM to Fisher’s equation leads to calculation of unneeded terms and more time consumed in repeated calculations for series solutions. Therefore, we use MVIM for Fisher’s equation to overcome these disadvantages.

The variational iteration method (VIM) has been applied to solve many functional equations, so far. In this paper the problem of conversion of three radioactive materials has been studied. By mathematical modeling of the problem a system of ordinary differential equations has been derived. The variational iteration method is applied to obtain exact solution of this system of ordinary differential equations.

In this paper, several D and strong convergence theorems are established for the Ishikawa iterations for nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and improve the corresponding results given by many authors.