JOURNAL OF MATHEMATICAL EXTENSION
Year:2010 | Volume:4 | Issue:2 (S.N. 8)|Papers Count:10

In this paper we introduce a new extension to Hahn-Banach Theorem and consider its relation with the linear operatres. At the end we give some applications of this theorem.

In this paper by using the notion of T-distance, we will prove Mizoguchi-Takahashi's fixed point theorem, which is a general-ization of fixed point theorem which has been given by Nadler.

Stochastic differential equations (SDEs), arise from physical systems that possess inherent noise and certainty. We derive a SDE for electrical circuits. In this paper, we will explore the close relationship between the SDE and autoregressive (AR) model. We will solve SDE related to RC circuit with using of AR (1) model (Markov process) and however with Euler-Maruyama (EM) method. Then, we will compare this solutions. Numerical simulations in MATLAB are obtained.

In this paper, by using of C*-algebra we give a metric with range in positive unit ball of a C*-algebra. Indeed this is a generalization of a fuzzy metric space. Some deFInitions of compatible mappings of types (I) and (II) are introduced and some FIxed and common FIxed point theorems are proved.

An operator T on a Banach space X is said to be weakly hypercyclic if there exists a vector x Î X whose orbit under T is weakly dense in X. We show that every weakly hypercyclic composition operator on classic Hardy space H2 is norm hypercyclic.

In this paper, a numerical method for solving the nonlinear Fredholm integral equation is presented. We intend to approximate the solution of this equation by quadrature methods and by doing so, we solve the nonlinear Fredholm integral equation more accurately. Several examples are given at the end of this paper.

Using the concept of possibility proposed by zadeh, luhand- jula ([4, 8]) and buckley ([1]) have proposed the possibility programming.The formulation of buckley results in nonlinear programming problems.Negi [6] re-formulated the approach of Buckley by the use of trapezoidal fuzzy numbers and reduced the problem into fuzzy linear programming problem. Shih and Lee ([7]) used the Negi approach to solve a minimum costoow problem, whit fuzzy costs and the upper and lower bound. In this paper we shall consider the general form of this problem where all of the parameters and variables are fuzzy and also a model for solving is proposed.

An application of the Exp-function method (EFM) to search for exact solutions of nonlinear partial differential equations is analyzed. This method is used for the modified KdV equation and the generalized KdV equation. The EFM was used to construct peri- odic wave and solitary wave solutions of nonlinear evolution equations (NLEEs). This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the Exp-function method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics and applied mathematics.

Let S be an inverse semigroup with an upward directed set of idempotents E. In this paper we prove that if S is amenable, then l1(S) Ä^ l1(S) is module amenable as an l1(E)-module. Also we show that L1(S) Ä^ l1 (S) is module super-amenable if an appropriate group homomorphic image of S is finite.

In this paper, the continuse Legendre wavelets constructed on the interval [0, 1] are used to solve the nonlinear Fredholm integro-differential equation. The nonlinear part of integro-differential is ap- proximated by Legendre wavelets, and the nonlinear integro-differential is reduced to a system of nonlinear equations. We give some numerical examples to show applicability of the proposed method.