JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2019 | Volume:5 | Issue:18 |Papers Count:13

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-continuous L-type mappings and upper semi-continuous quasi-nonexpansive mappings. We study relationships between MD-type mappings and some other set-valued generalization of nonexpansive mappings. In the sequel we show that if E is a nonempty, weakly compact and convex subset of a Banach space (X, ‖ . ‖ ) for which every D-type self-mapping on E has a fixed point, then every MD-type self-mapping on E has a fixed point. This result gives a partial affirmative answer to an open problem of Rich. Moreover, we establish some fixed theorems for MD-type mappings which generalize some well-known results in the literature.

Let-----. For an analytic self-map---of---, Let---be the composition operator with composite map---so that----. Let---be a bounded analytic function on---. The weighted composition operator---is defined by---. Suppose that---is the Hardy space, consisting of all analytic functions defined on---, whose Maclaurin cofficients are square summable. . . . . .

In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.

In this paper, we introduce the new concept of biprojectivity of a Banach algebra modulo an ideal, as a generalization of this notion in the classical case. By using it, we obtain some necessary and sufficient conditions for contractibility of Banach algebras modulo an ideal. In particular we characterize the contractibility of quotient Banach algebras. Also we study the relationship between the biprojectivity modulo an ideal of a Banach algebra and the biprojectivity of the corresponding quotient Banach algebra.

One of the most complicated decision making problems for managers in supply chain is the evaluation of supply chain performance which can be done in different ways. Though several studies have been developed on supply chain performance evaluation based on balanced scorecard (BSC), a few studies focused on relationships among four perspectives of BSC. This paper focuses on these relationships, especially on relationships with feedback structures. For this purpose, after identification of the BSC’ s more important factors in evaluation of the suppliers, DEMATEL technique is employed to determine feedback relationships among these factors and to attain to the critical factors from the influential and to be influenced point of view. Next, these factors are used as the inputs and outputs of data envelopment analysis (DEA) weak disposability model in presence of undesirable factors to evaluate the suppliers and determine their efficiency scores. Finally, the efficient units were ranked based on the Anderson-Peterson (AP) super efficiency model. The proposed procedure is applied as a framework to evaluate the suppliers of Pars Khazar Company.

In this paper, we present a block version of incomplete LU preconditioner which is computed as the by-product of block A-biconjugation process. The pivot entries of this block preconditioner are one by one or two by two blocks. The L and U factors of this block preconditioner are computed separately. The block pivot selection of this preconditioner is inherited from one of the block versions of Gaussian elimination process. The main basis to propose such a block preconditioner is a connection between the Gaussian elimination process and the A-biconjugation algorithm. In the numerical experiment section, we have generated artificial linear systems. Then, we have computed the block and plain versions of this incomplete LU preconditioner. We have used these two preconditioners as the right preconditioner for linear systems. After that, the GMRES(50) method has been applied to solve the right preconditioned systems. The results indicate that the block preconditioner gives fewer number of iterations of GMRES(50) method than the plain version. Therefore, the block preconditioer has a better quality.

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal.

Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the presentation of Black-Scholes model in 1973, attracted the attention of economists to the partial differential equations more than past. Therefore, we need a simple and precise solution for this kind of partial differential equations to determine the pricing option contracts. In this article the cubic B-spline collocation method has been used in the form of a difference method to solving Black-Scholes partial differential equation. Using this method as simplicity as finite difference method and does not have complex computation of traditional B-spline collocation method. The use of this method leads to a system of tridiagonal algebraic equations which is suitable for computer programming. The stability and convergence of this method is discussed and numerical results are presented for European and American options.

The full ranking or complete ranking of decision making units is one of the main issues in data envelopment analysis. A full ranking is a ranking that considers all efficient and inefficient units simultaneously and finds a ranking for them. Almost all of the developed ranking methods consider only the efficient units. On the other hand, ranking inefficient units by traditional data envelope analysis models are also inaccurate due to ignoring the role of slacks. In the present paper two novel methodologies are proposed in order to fully ranking of decision making units. In the presented approach, all of the decision making units participate in a competition in a way that all are projected onto the efficient frontier considering common weights. Then, according to the profit that each unit attains to reach this standard level, a rank order of all decision making units are obtained. In the first method, the satisfaction of units is measured in the competition and the satisfaction of the units that have the lowest satisfaction is improved. in the second method, by setting up the cross-profit table, the optimal weights of all units are taken into account in competition. After all, the proposed methods are applied on sample problems.

The Supply Chain is considered a necessity for the success of organizations seeking the most economic, environmental and social impacts. In addition, the implementation and suitable execution of this supply chain seems to be necessary. Considering the importance of the social impacts of this supply chain, a fuzzy multi-objective mathematical model is provided such that, in addition to considering the environmental and economic impacts, social impacts are also considered. In order to approximate the provided model to real-world conditions, some parameters are considered under conditions of uncertainty and in the form of triangular fuzzy numbers. A two-step method is provided to solve the proposed model. In the first step, the model converges to a determinate multi-objective problem using the necessity measure and in the second step the model is solved using the cumulative function method. Finally, to show the applicability of the proposed method, a real industrial case study is provided.

In this paper, a two stages method to determine suitable benchmark and return scale of the decision making units set is presented. At first, all of the efficient reference set in no radial data envelopment analysis (DEA) based on linear programming is found. first, RAM model is introduced and units is investigated using this model, then, to run the given algorithm below steps is performed. At the first step, the type of reference set is introduced and at the second step, a unique linear programming problem based on primal dual method is proposed to know all of the possible reference sets for a decision making unit. At the third step, return to scale in the no radial DEA method is measured. Ultimately, girls high school of shiraz city one zone efficiency is investigated to show to be applicate of this method and suitable benchmark and return scale is presented for this set of decision making units.

In this paper fully fuzzy linear programming (FFLP) problem with both equality and inequality constraints is considered where all the parameters and decision variables are represented by non-negative trapezoidal fuzzy numbers. According to the current approach, the FFLP problem with equality constraints first is converted into a multi– objective linear programming (MOLP) problem with crisp constraints and then a lexicographic ordering method is used for solving the resulting MOLP problem. However, this approach cannot be used for finding the fuzzy optimal solution of FFLP problems with inequality constraints. The aim of this study is to point out and correct some errors in the definitions, notations operations and fuzzy ordering of the current approach for solving FFLP problems with fuzzy inequality constraints. Hence, a modified approach to obtain the fuzzy optimal solution of the FFLP problems with inequality constraints is proposed. Finally, several numerical examples are presented to illustrate the proposed approach.