Theory of Approximation and Applications
Volume:7 Issue: 2, Summer and Autumn 2012

We shall prove an existence inequality for two maps on Banach algebra, with an example and in sequel we have some results on R and Rn spaces. This way can be applied for generalization of some subjects of mathematics in teaching which how we can extend a math problem to higher level.

In this paper, we nd the relationships between module contractibility of a Banach algebra and its ideals. We also prove that module contractibility of a Banach algebra is equivalent to module contractibility of its module uniti- zation. Finally, we show that when a maximal group homomorphic image of an inverse semigroup S with the set of idempotents E is nite, the module projective tensor product `1(S)b `1(E)`1(S) is `1(E)-module contractible.

This research proposes a methodology for ranking decision making units by using a goal programming model.We suggest a two phases procedure. In phase 1, by using some DEA problems for each pair of units, we construct a pairwise comparison matrix. Then this matrix is utilized to rank the units via the goal programming model.

In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted to nd the solution. To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization method to obtain the stable numerical approximation to the solution. Some numerical experiments con-rm the utility of this algorithm as the results are in good agreement with the exact data.

In this paper, a numerical method for nding minimal solution of a mn fully fuzzy linear system of the form ~ A~x = ~b based on pseudo inverse calculation, is given when the central matrix of coecients is row full rank or column full rank, and where A~ is a non-negative fuzzy mn matrix, the unknown vector ~x is a vector consisting of n non-negative fuzzy numbers and the constant ~b is a vector consisting of m non-negative fuzzy numbers.

In this paper, we prove the existence of the solution for boundary value prob-
lem(BVP) of fractional di erential equations of order q 2 (2; 3]. The Kras-
noselskii's xed point theorem is applied to establish the results. In addition,
we give an detailed example to demonstrate the main result.

The main attempt of this article is extension the method so that it generally would be able to consider the classical solution of the systems and moreover,produces the optimal trajectory and control directly at the same time. There-fore we consider a control system governed by a bone marrow cancer equation.
Next, by extending the underlying space, the existence of the solution is con-sidered and pair of the solution are identied simultaneously. In this mannera numerical example is also given.

In this work, we present a numerical method for solving nonlinear Fredholm and Volterra integral equations of the second kind which is based on the use of Block Pulse functions(BPfs) and collocation method. Numerical examples show eciency of the method.

This paper proposes a three-step method for solving nonlinear Volterra integral equations system. The proposed method convents the system to a (3  3) nonlinear block system and then by solving this nonlinear system we nd approximate solution of nonlinear Volterra integral equations system. To show the advantages of our method some numerical examples are presented.