Journal of Mathematical Extension
Volume:16 Issue: 4, Apr 2022

In this paper, we present a detailed study of the following difference equation x_n+1 = αn 1 + x_nx_n−1 , n ∈ N0, where the sequence (αn)n≥0 is positive, real, periodic with period two and the initial values x−1, x0 are nonnegative real numbers. By this study, we determine global behavior of p

Let Gk,n be the Grassmann manifold of k-planes in Rn+k . The Lusternik-Schnirelmann category and topological complexity are important invariants of topological spaces. In this note we calculate the Lusternik-Schnirelmann category and topological complexity of cer- tain products of Grassmannian manifolds by using cup and zero-cup length. Also we will find the lower and upper bounds of the topological complexity of some Grassmannian manifolds by the same method.

Evaluation and selection of efficient suppliers is accepted as one of the key issues in supply chain management (SCM). The research problem here is a specific mode of suppliers in a supply chain with a multistage system, consisting of several components. Each component is also regarded as a phase in a supply-chain network (SCN) with a number of inputs and outputs that are being produced independently and simultaneously. Moreover, each input is generated from different modes and there are many output indicators. The main purpose of this study is to propose a new method for selecting the most appropriate suppliers in a SCN using data envelopment analysis (DEA) strategies. The premise is that, a SCN space can be transformed into a DEA one considering the occurrence of input/output mode in each phase in the SCN as a decision-making unit (DMU), and the relative efficiency of each possible mode in each phase of the given network can be obtained via DMUs. Finally, the component endowed with the highest efficiency can be selected as the most appropriate supplier.

In this paper, we first study fuzzy subgroups and fuzzy multigroups of a group G and we obtain some chains of fuzzy subgroups of a fuzzy subgroup and by these sequences, we construct fuzzy multi- groups. We show that there is a relationship between a fuzzy multigroup with underlying group G and a fuzzy multigroup with underlying group Aut(A). Moreover, we generate a code by using the defined special fuzzy multigroup automorphisms.

Data envelopment analysis (DEA) evaluates the cost effi- ciency of systems with multiple inputs and multiple outputs in two sce- narios, one where the input prices are the same in all decision-making units (DMUs) (competitive space), and the other where the input prices differ from one DMU to another (non-competitive space). In many sit- uations, the DMUs could have a multi-stage network structure with intermediate measures. Although a model has been presented for calcu- lating the network cost efficiency in a competitive space in such cases, no method has been proposed so far to calculate the cost efficiency of such networks in a non-competitive space. The present article focuses on the concept of cost efficiency in DEA for DMUs with network struc- tures and varying input prices. To this end, a cost-based production possibility set (PPS) is first introduced for the network systems and their sub-systems, and after calculating the network cost efficiency, it is decomposed into efficiencies such as technical, price, and allocative efficiencies, and the reasons behind the occurrence of extra costs due to various types of inefficiency are explained.

In this paper, we will investigate the existence of some solutions for a multi singular fractional differential system with some boundary conditions.

We introduced the notions of locally quasiconvex spaces and quasi-seminorms, and investigate the natural relationships between these two notions. As applications, we obtain generalizations of some well known fixed point theorems and fixed set theorems that require neither metrizability, nor compactness nor the standard notion of con- vexity.

n this paper, under growth conditions on the nonlinearity, we obtain the existence of at least three weak solutions for some singular elliptic problems involving the p-Laplacian, subject to Dirichlet bound- ary conditions in a smooth bounded domain in RN . The approach is based on variational methods and critical point theory.

This paper is devoted to obtaining an analytical solution for the second-order fuzzy differential equations by considering the type of generalized Hukuhara differentiability of the solution. The effective- ness and efficiency of the approaches are illustrated by solving several practical examples such as the fuzzy Cauchy-Euler equation, the fuzzy Legendre equation, and the fuzzy Chebyshev differential equation.

Let B(H) denote the algebra of all bounded linear opera- tors acting on a complex Hilbert space H. For A, B ∈ B(H), define the bimultiplication operator M2,A,B on the class of Hilbert-Schmidt oper- ators by M2,A,B (X) = AXB. In this paper, we show that if B∗, the adjoint operator of B, is hyponormal, then co(W0(A)W0(B)) ⊆ W0(M2,A,B ), where co stands for the convex hull and W0(.) denotes the maximal numerical range. If in addition, A is hyponormal, we show that co(W0(A)W0(B)) = W0(M2,A,B ).