Journal of Mathematical Extension
Volume:8 Issue: 1, Winter 2014

In this paper, we study weakly compact left multipliers on the Banach algebra LUC(G). We show that G is compact if and only if there exists a non-zero weakly compact left multipliers on LUC(G). We also investigate the relation between positive left weakly completely continuous elements of the Banach algebras LUC(G) and L1(G). Finally, we prove that G is finite if and only if there exists a non-zero multiplicative linear functional μ on LUC(G) such that μ is a left weakly completely continuous elements of LUC(G).

In this paper, we interpret a two-point initial value problem for a second order fuzzy differential equation. We investigate a problem of finding a numerical approximation of the solution by using fuzzy neural network. Here neural network is considered as a part of a larger field called neural computing or soft computing. Finally, we illustrate our approach on an applied example in engineering.

In this paper, the analytical solution of the space-and timefractional Fokker-Planck equation was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made, the comparisons show that the homotopy analysis method is very effective and convenient. An optimal value of the convergence control parameter is given through the square residual error. By minimizing the the square residual error, the optimal convergence-control parameters can be obtained. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results.

This study has considered the problem of finding best proximity pair in fuzzy metric spaces and uniformly convex fuzzy Banach spaces for fuzzy cyclic contraction map. We prove the uniqueness of this point in uniformly fuzzy Banach spaces. We also give an algorithm to find a best proximity point for the map S in setting of a uniformly convex fuzzy Banach spaces.

We prove an operator arithmetic-harmonic mean type inequality in Krein space setting, by using some block matrix techniques of indefinite type. We also give an example which shows that the operator arithmetic-geometric-harmonic mean inequality for two invertible selfadjoint operators on Krein spaces is not valid, in general.

This paper presents a modification of successive approximation method by using projection operator to solve nonlinear Volterra- Hammerstein integral equations of the second kind. In this paper, it is proved that under some conditions the sequence of iterated solutions converges to the exact solution. Applicability of this modification has been shown with some numerical examples. Comparisons with some other methods are also addressed which highlight superiority of the method.

The aim of this paper is to introduce the notion of discrete and inverse discrete weighted transform. We show that discrete input data can be converted to a continuous approximation through the inverse discrete weighted transform.

In this paper a numerical procedure based on mollification approach and conjugate gradient method is established to solve a one dimensional inverse moving boundary value problem. The problem is considered with noisy data. A regularized problem using mollification approach is considered and the conjugate gradient method is used to solve the proposed problem. Some numerical examples are considered to show the ability of this method. These examples show that the accurate and stable results can be obtained efficiently for these kind of problems.