Sahand Communications in Mathematical Analysis
Volume:4 Issue: 1, Summer-Autumn 2016

An object X of a category C with finite limits is called exponentiable if the functor −×X:C→C has a right adjoint. There are many characterizations of the exponentiable spaces in the category Top of topological spaces. Here, we study the exponentiable objects in the category STop of soft topological spaces which is a generalization of the category Top. We investigate the exponentiability problem and give a characterization of exponentiable soft spaces. Also we give the definition of exponential topology on the lattice of soft open sets of a soft space and present some characterizations of it.

In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature formula to reduce the fractional optimal control problem to solving a system of nonlinear algebraic equations that greatly simplifies the problem. Finally, some examples are included to confirm the efficiency and accuracy of the proposed method.

In this paper, a numerical solution for a system of linear Fredholm integro-differential equations by means of the sinc method is considered. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. The exponential convergence rate O(e−kN√) of the method is proved. The analytical results are illustrated with numerical examples that exhibit the exponential convergence rate.

A generalization of the known results in fusion frames and g-frames theory to continuous fusion frames which defined by M. H. Faroughi and R. Ahmadi, is presented in this study. Continuous resolution of the identity (CRI) is introduced, a new family of CRI is constructed, and a number of reconstruction formulas are obtained. Also, new results are given on the duality of continuous fusion frames in Hilbert spaces.

Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given and the efficiency and accuracy are illustrated by applying the method to some examples.

Double system of exponents with complex-valued coefficients is considered. Under some conditions on the coefficients, we prove that if this system forms a basis for the Morrey-Lebesgue type space on [−π,π] , then it is isomorphic to the classical system of exponents in this space.

In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results to the case of comonotone functions.

In this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of A.P. Sostak's and Ramadan is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.