In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern,  Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper...

Suppose that (Lm)m≥1 is a given sequence of linear and positive operators. Starting with the mentioned sequence, the new sequence (Km)m≥1 of linear and positive operators is constructed. For the operators (Km)m≥1 a convergence theorem and a Voronovskaja-type theorem are established. As particular cases of the general construction, we refined the Bernstein’s operators, the Stancu’s operators, th...

Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow for instance quadratically in the fibers outside of a compact set, one can define Floer homology and show that it is naturally isomorphic to singular homology of the free loop space. We review the three isomorphisms construc...

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces

In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved.

We investigate the convergence of Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with the Fréchet differentiable norm. Our results improve and extend the results obtained by Marino-Xu, Zhou, Osilike-Udomene, Zhang-Guo and the corresponding results. We also point out that the condition given by ChidumeShahzad 2010 is not satisfie...

In this paper, we propose a new tool based on Observed Time Difference of Arrival (OTDOA) technique in order to estimate both the position of the different User Equipments (UEs) and the Relative Time Differences (RTDs) between Node Bs in real UMTS networks from measurements reports providing the TM parameter and the locations of the sites. This technique results in a non-linear least squares es...

Orthogonal/vector approximate message-passing (AMP) is a powerful (MP) algorithm for signal reconstruction in compressed sensing. This paper proves the convergence of Bayes-optimal orthogonal/vector AMP large system limit. The proof strategy based on novel long-memory (LM) MP approach: A first step construction LM-MP that guaranteed to converge systematically. second large-system analysis via a...