Mathematics

In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS). This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.

The aim of this paper is proposing a new approach for finding all solutions of system of nonlinear fuzzy equations using Fuzzy Linear Programming (FLP). This approach is based on the FLP test for nonexistence of a solution to a system of fuzzy nonlinear equations using fuzzy simplex method. Also a numerical example has proposed to show the applicability of the method.

Linear programming models play an important role in management,
economic, data envelopment analysis, operations research and many industrial
applications. In many practical situations there is a kind of ambiguity in the
parameters of these models which can be expressed by means of fuzzy
numbers. In the literature of fuzzy mathematical programming there are many
types of the fuzzy linear programming problems. But in this paper, we deal
with a kind of linear programming which includes the triangular fuzzy numbers
in its parameters. For finding the solution of these problems, we propose a
revised simplex algorithm for an extended linear programming problem which
is equivalent to the original fuzzy linear programming problem. An illustrative
example is presented to clarify the proposed approach. A fuzzy DEA model has
been also considered as a practical application to illustrate the effectiveness of
the proposed approach.

Some new concepts in regards to $\bar{\alpha}$-feasibility and $\bar{\alpha}$-efficiency of solutions in fuzzy mathematical programming problems are introduced in this paper, where $\bar{\alpha}$ is a vector of distinct satisfaction degrees. Based on the defined concepts, a new method is suggested to solve fuzzy mathematical programming problems. In this sense, the proposed approach enables decision makers to take into account more flexible solutions by allowing desired distinct satisfactions in constraints. In the case of linear problems with fuzzy constraints, multi-parametric programming is employed to obtain the optimal solution as an affine function of distinct satisfaction degrees. In particular, it proves that the obtained solution is convex and continuous. Therefore, the different optimal solutions can be obtained by a simple substituting the new values of satisfaction parameters into the parametric profiles without any further optimization
calculations, which is desirable for online optimization and sensitivity analysis of the profit to satisfaction parameters.

This paper deals with some results in generalized convex spaces. The notion of minimal generalized convex space is introduced and then two well known results in nonlinear analysis, that is the open and closed versions of Fan-KKM principle in this new setting are considered. Indeed, it is shown that, for any m-closed(m-open) valued KKM map F : D X in a minimal generalized convex space (X, D, Γ), {F (z) : z ∈ D} has the finite intersection property.

This paper deals with some fixed point and maximal element theorems via transfer closed, KKM multimaps in minimal generalized convex spaces. Moreover, some generalized versions of Fan-KKM principle for transfer closed multimaps are given. Nonlinear

This paper aims at establishing the existence of results for a nonstandard equilibrium problems (EPN). The solutions of this inequality are discussed in a subset K (either bounded or unbounded) of a Banach spaces X. Moreover, we enhance the main results by application of some differential inclusion.

This paper is devoted to introduce the concepts of transfer closed and transfer open multimaps in minimal spaces. Also, some characterizations of them are considered. Further, the notion of minimal local intersection property will be introduced and characterized. Moreover, some maximal element theorems via minimal transfer closed multimaps and minimal local intersection property are given.

This paper aims at establishing the existence of results for a nonstandard equilibrium problems $(EP_{N})$. The solutions of this inequality are discussed in a subset $K$ (either bounded or unbounded) of a Banach spaces $X$. Moreover, we enhance the main results by application of some differential inclusion.

This paper is devoted to introduce the concepts of transfer closed and transfer open multimaps in minimal spaces. Also, some characterizations of them are considered. Further, the notion of minimal local intersection property will be introduced and characterized. Moreover, some maximal element theorems via minimal transfer closed multimaps and minimal local intersection property are given.

In this paper, we are concerned with the existence of a solution u 2 K for the variational inequality problem $ V I(A; psi, phi, g;K)$. Furthermore, we propose some conditions that ensure the well-posedness of this problem. We study an operator type $g - ql$ which extends the linear problem. Finally, we investigate the existence of solutions for general vector variational inequalities in the inclusion form.

In this paper, we are concerned with the existence of a solution u ∈ K for the variational inequality problem V I(A,ψ, φ, g,K). Furthermore, we propose some conditions that ensure the well-posedness of this problem. We study an operator type g − ql which extends the linear problem. Finally, we investigate the existence of solutions for general vector variational inequalities in the inclusion form.

Some new classes of extended general nonconvex set-valued variational inequalities and the extended general Wiener-Hopf inclusions are introduced. By the projection technique, equivalence between the extended general nonconvex set-valued variational inequalities and the fixed point problems as well as the extended general nonconvex Wiener-Hopf inclusions is proved. Then by using this equivalent formulation, we discuss the existence of solutions of the extended general nonconvex set-valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set-valued variational inequalities. We also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set-valued variational inequalities. The results presented in this paper extend and improve some known results from the literature.

J. K. Brooks and P. W. Lewis have established that if E and E * have RNP, then in M (Σ, E), m n converges weakly to m if and only if m n (A) converges weakly to m(A) for each A ∈ Σ. Assuming the existence of a special kind of lifting, N. Randrianantoanina and E. Saab have shown an analogous result if E is a dual space. Here we show that for the space M (P(N), E) where E * is a Grothendieck space or E is a Mazur space, this kind of weak convergence is valid. Also some applications for subspaces of L(E, F ) similar to the results of N. Kalton and W. Ruess are given.

Suppose $\Pi_1(E, F)$ is the space of all absolutely 1-summing operators between two Banach spaces $E$ and $F$. We show that if $F$ has a copy of $c_0$, then $\Pi_1(E, F)$ will have a copy of $c_0$, and under some conditions if $E$ has a copy of $\ell_1$ then $\Pi_1(E, F)$ would have a complemented copy of $\ell_1$.

Furrow irrigation is one of the most common methods of surface irrigation. Its hydraulic behaviour is influenced by the inflow hydrograph shape. The performance of furrow irrigation system can be improved through optimal management practices such as selecting the correct inflow rates, inflow hydrographs and cut-off times. The biggest obstacle in improving the performance of furrow irrigation is the difficulty in estimating the infiltration function, especially under different furrow inflow hydrographs. This study was performed to investigate a multilevel calibration of furrow infiltration, and roughness coefficient, for furrow irrigation using three different furrow inflow hydrograph shapes such as constant, cutback and cablegation using a zero-inertia model and verifying the results with the field data. The results showed that the multilevel calibration method adopted here estimated the Kostiakov-Lewis infiltration equation parameters and roughness coefficient more precisely than the two-point method for different furrow inflow hydrograph shapes. The infiltration equation developed by the method simulated the field data more accurately than the two-point method with the zero-inertia model. The multilevel calibration method predicted the total volume of runoff, total volume of infiltration and furrow outflow hydrograph shapes with lower relative errors compared to the twopoint method for the different furrow inflow hydrograph shapes. (B. Mostafazadeh-Fard).