Journal of Mathematical Extension
Volume:6 Issue: 1, Winter 2012

In this paper, we study a new enlargement of subdifferential for any proper lower semicontinuous function. We know that ε-subdifferential of any proper lower semicontinuous function is an enlargement of its subfifferential and any point from the graph of ε-subdifferential can be approximated by a point from the graph of sub- fifferential. This nice property, apart from its theoretical importance, gives also the possibility to use the enlargement of subdifferentials in finding approximate solutions of inclusions determined by subdifferentials. We define a new enlargement and observe, in the case subdiffer- entials, the relation between this new enlargement and the ε-subdiffer- ential.

We characterize bounded and compact generalized composition operators between Bloch type spaces and weighted Dirichlet type spaces. Then, we show that these results can be employed to characterize bounded and compact Volterra type operators between these spaces. Finally, we give a connection between weighted and generalized composition operators to conclude some results about boundedness and compactness of them.

In this paper, a new three-step iterative method for finding a simple root of the nonlinear equation of f(x) = 0 will be introduced. This method is based on the two-step method of [C. Chun, Y. Ham, Some fourth-order modifications of Newton’s method, Appl. Math. Comput. 197 (2008) 654-658]. The new method requires three evaluations of the function and two of its first-derivative. We will prove that the order of convergence of the new method and its efficiency index will respectively be 8, and 1.5157. Some numerical experiments are given to illustrate the performance of the three-step iterative method.

In this work, the modified Laplace Adomian decomposition method (LADM) is applied to solve the integro-differential equations. In addition, examples that illustrate the pertinent features of this method are presented, and the results of the study are discussed. We prove the convergence of LADM applied to the integro-differential equations. Also, the results show that the introduced method is a powerful tool for solving the integro-differential equations.

Let σ be a linear mapping from a dense subalgebra A of a Banach algebra B into B. In this note, we study the closability of a module σ− derivation δ from A into a B− bimodule M. Applying the notions of torsion-free modules and essential ideals, we present several results concerning the closability of such derivations. Also we investigate the closability of module σ− derivations of the C∗− algebra B into a Hilbert B− bimodule M.

In this paper, normal equations for singular fuzzy linear systems is proposed. The principal application of the normal equations is to systems of equations that are inconsistent. The results are explained by solving some numerical examples.

This article is a continuation of E. Momtahan’s work in which he studied the literature via countable injectivity. Along this line, א0-Ikeda-Nakayama rings have been studied and among other things, new characterizations of basically disconnected and extremally discon- nected spaces have been given. Furthermore we will observe that a boolean ring is א0-self-injective if and only if it is an א0-IN ring.

This paper suggests a method of finding super-efficiency scores and modification of input-oriented models for sensitivity analysis of decision making units. First, by using DEA-R (ratiobased DEA) models in the input orientation, the models of superefficiency and also models of super-efficiency modification are suggested. Second, the worst-case scenarios are considered where the efficiency of the test DMU is deteriorating while the efficiencies of the other DMUs are improving. Then, by combining these two ideas, a model is suggested which increases the super-efficiency score and modifies the change ranges in order to preserve the performance class. In the end, the super-efficiency and change interval of efficient decision making units for 23 branches of Zone 1 of the Islamic Azad University are calculated.