Journal of Mathematical Extension
Volume:12 Issue: 2, Spring 2018

In this paper we consider shadowing and weak shadowing properties for iterated function systems IFS and give some results on these concepts. At first, a sufficient condition for shadowing property is given and by this result we present two IFS which have the shadowing property. It is proved that every uniformly expanding as well as every uniformly contracting IFS has the weak shadowing property. By an example we show that in IFS’s shadowing property does not imply weak shadowing property. Finally we have the main result of the paper and prove that the weak shadowing is a generic property in the set of all IFS’s.

In this paper, first, a numerical method is presented for solving generalized linear and nonlinear Lane-Emden type equations. The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions. This matrix with the tau method is then utilized to transform the differential equation into a system of algebraic equations. Finally, the convergence analysis is investigated and the efficiency of the proposed method is indicated by some numerical examples

Identifying the efficient extreme units in a production possibility set is a very important matter in data envelopment analysis, as these observed, real units have the best performances. In this paper, we proposed a multiple objective programming model, in which the feasible region is the production possibility set under the assumption of variable returns to scale and the objective function consists of input and output variables. As we know, by increasing the dimensions of the problem, the set of efficient points would increase as well; thus, using the multiple objective linear programming problem-solving methods in a decision set would lead to computational problems and it would be much easier to work in the outcome set instead of the decision set. In this research, we show that the efficient points in the outcome set of the suggested multiple objective linear programming problems correspond with the efficient extreme points in data envelopment analysis. An outer approximation algorithm is presented for production of all efficient extreme points in the outcome set. This algorithm provides us with the equations for all efficient surfaces. In the outcome set, this algorithm would use few calculations to produce all the extreme points. Finally, we demonstrate the presented approach through numerical examples.

We introduce the notion of J-Armendariz rings, which are a generalization of weak Armendariz rings and investigate their properties. We show that local rings are J-Armendariz. Also, we prove that a ring R is J-Armendariz if and only if R[[x]] is J-Armendariz. It is shown that the J-Armendariz property is not Morita invariant. As a specific case, we show that the class of J-Armendariz rings lies properly between the class of one-sided quasi-duo rings and the class of perspective rings.

‎One of the first constructions of algebra is the quotient field of a commutative integral domain,constructed as a set of fractions‎, ‎which can lead to a very useful technique in commutative ring theory‎. ‎In this article the researchers considered rings of fractions for gamma rings and some new characterizations were developed in gamma rings of fractions‎. ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

In this paper we establish a refinement and some reverses forJensens inequality for the general Lebesgue integral on divisions of measurablespace. Applications for discrete inequalities and weighted means of positivenumbers are also given. Some examples related to Hermite-Hadamard inequal-ity for convex functions are provided as well.

Differintegral theorems are applied to solve some ordinary differential equations and fractional differential equations. By using these theorems, we obtain different results in the fractional differintegral forms. In this paper, we aim to solve the radial Schrödinger equation under the potential $ V(r)=H/r^{2}-K/r+Lr^{\kappa} $ in $ \kappa=0,-1,-2 $ cases. We also obtain the solutions in the hypergeometric form.

The purpose of this paper is to show that under reasonable assumptions Debrunner and Flor Theorem can be extended to arbitrary θ-monotone operators. This generalization provides some tools for further analysis of the θ-monotone operators, which allows us for establishing some key facts related to domains and ranges of θ-maximal monotone operators.