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 aHilbert module over a pro-C*-algebra A.

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 aHilbert module over a pro-C*-algebra A.

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

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

Image restoration has been an active research area. Dierent formulations are eective in high qualityrecovery. Partial Dierential Equations (PDEs) have become an important tool in image processingand analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kindof anisotropic diusion (ANDI) lter. Anisotropic diusion lter has become a valuable tool indierent elds of image processing specially denoising. This lter can remove noises without degradingsharp details such as lines and edges. It is running by an iterative numerical method. Therefore, afundamental feature of anisotropic diusion procedure is the necessity to decide when to stop theiterations. This paper proposes the modied stopping criterion that from the viewpoints of complexityand speed is examined. Experiments show that it has acceptable speed without suering from theproblem 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, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.