This paper investigates optimal error bounds and convergence rates for general Mann iterations computing fixed-points of non-expansive maps. We look that achieve the smallest fixed-point residual after n steps, by minimizing a worst-case bound $$\Vert x^n-Tx^n\Vert \le R_n$$ derived from nested family transport problems. prove this is tight so $$R_n$$ yields iterations. Inspired numerical resul...

In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is appli...

We provide an ultrafilter proof of the 2-dimensional Halpern–Läuchli Theorem in the following sense. If T0 and T1 are trees and T0 ⊗ T1 denotes their level product, we exhibit an ultrafilter U ∈ β(T0 ⊗ T1) so that every A ∈ U contains a subset of the form S0 ⊗ S1 for suitable strong subtrees of T0 and T1. We then discuss obstacles to extending our method of proof to higher dimensions.

In this paper, a Van der Pol oscillator containing a periodic oscillator is considered. A simple and effective iteration procedure to search the solution of the modified Van der Pol oscillator equation is proposed. This procedure is a powerful tool for determination of periodic solution of a non-linear equation of motion. The solutions obtained using the present iteration procedure are in good ...

Abstract We show the nonlinear ergodic theorem for monotone 1-Lipschitz mappings in uniformly convex spaces: if C is a bounded closed subset of an ordered space ( X , ∣·∣, ⪯), T : → mapping and x ⪯ ), then sequence averages 1 n ∑ i</m...

Analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. According to this, an impressive analytical method which is called Modified Iteration Perturbation Method (MIPM) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. This new method is combined by the Mickens and Iteration methods. Moreover, this method don...

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the multiple traveling salesman problem (mtsp) involves scheduling m > 1 salesmen to visit a set of n > m nodes so that each node is visited exactly once. the objective is to minimize the total distance traveled by all the salesmen. the mtsp is an example of combinatorial optimization problems, and has a multiplicity of applications, mostly in the areas of routing and scheduling. in this paper,...

We continue here [Sh276] (see the introduction there) but we do not relay on it. The motivation was a conjecture of Galvin stating that 2 ω ≥ ω 2 + ω 2 → [ω 1 ] n h(n) is consistent for a suitable h : ω → ω. In section 5 we disprove this and give similar negative results. In section 3 we prove the consistency of the conjecture replacing ω 2 by 2 ω , which is quite large, starting with an Erd˝ o...