this paper presents an efficient modification of the variational iteration method for solvingboundary value problems using the chebyshev polynomials. the proposed method can be applied to linearand nonlinear models. the scheme is tested for some examples and the obtained results demonstrate thereliability and efficiency of the proposed method.

Let D be a subset of a normed space X and T : D → X be a nonexpansive mapping. In this paper we consider the following iteration method which generalizes Ishikawa iteration process: xn+1 = t (1) n T (t (2) n T (· · ·T (t (k) n Txn + (1− t (k) n )xn + u (k) n ) + · · · ) +(1− t n )xn + u (2) n ) + (1− t (1) n )xn + u (1) n , n = 1, 2, 3 . . . , where 0 ≤ t (i) n ≤ 1 for all n ≥ 1 and i = 1, . . ...

Let q > 1 and E be a real q-uniformly smooth Banach space, K be a nonempty closed convex subset of E and T : K → K be a Lipschitz continuous mapping. Let {un} and {vn} be bounded sequences in K and {αn} and {βn} be real sequences in [0, 1] satisfying some restrictions. Let {xn} be the sequence generated from an arbitrary x1 ∈ K by the Ishikawa iteration process with errors: yn = (1− βn)xn + βnT...

We give a quantitative analysis of a result due to Borwein, Reich and Shafrir on the asymptotic behaviour of the general Krasnoselski-Mann iteration for nonexpansive selfmappings of convex sets in arbitrary normed spaces. Besides providing explicit bounds we also get new qualitative results concerning the independence of the rate of convergence of the norm of that iteration from various input d...

In this paper , we study the strong convergence of SP iterative scheme for quasi-contractive operators in Banach spaces. We show that Picard , Mann , Ishikawa , Noor, new two step and SP iterative schemes are equivalent for quasi-contractive operators. In addition, we show that the rate of convergence of SP iterative scheme is better than the other iterative schemes mentioned above for increasi...