Theory of Approximation and Applications
Volume:8 Issue: 2, Summer and Autumn 2013

In this paper, we generalize some results from Hilbert C*-modules to pro-C*- algebra case. We also give a new proof of the known result that l2(A) is a Hilbert module over a pro-C*-algebra A.

Although homotopy-based methods, namely homotopy analysis method and homotopy perturbation method, have largely been used to solve functional equations, there are still serious questions on the convergence issue of these methods. Some authors have tried to prove convergence of these methods, but the researchers in this article indicate that some of those discussions are faulty. Here, after criticizing previous works, a sucient condition for convergence of homotopy methods is presented. Finally, examples are given to show that even if the homotopy method leads to a convergent series, it may not converge to the exact solution of the equation under consideration.

Boujari [5] proved a fi xed point theorem with an old version of the integral type contraction, his proof is incorrect. In this paper, a new generalization of integral type contraction is introduced. Moreover, a fixed point theorem is obtained.

Image restoration has been an active research area. Di erent formulations are e ective in high quality recovery. Partial Di erential Equations (PDEs) have become an important tool in image processing and analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kind of anisotropic di usion (ANDI) lter. Anisotropic di usion lter has become a valuable tool in di erent elds of image processing specially denoising. This lter can remove noises without degrading sharp details such as lines and edges. It is running by an iterative numerical method. Therefore, a fundamental feature of anisotropic di usion procedure is the necessity to decide when to stop the iterations. This paper proposes the modi ed stopping criterion that from the viewpoints of complexity and speed is examined. Experiments show that it has acceptable speed without su ering from the problem of computational complexity.

The index of matrix A in Cn.n is equivalent to the dimension of largest Jor- dan block corresponding to the zero eigenvalue of A. In this paper, indicial equations and normal equations for solving inconsistent singular linear system of equations are investigated.