Journal of Mathematical Extension
Volume:11 Issue: 4, Autumn 2017

We present here, three- dimensional Haar wavelet based method for solving well known two- dimensional telegraph equation, by approximating higher order mixed derivatives by a series of higher dimensional Haar wavelet functions, which are integrated subsequently to get wavelet approximation of the solution. Numerical examples have been solved to illustrate the accuracy and efficiency of the proposed Haar wavelet method. High accuracy of the results even in the case of a small number of collocation points have been observed.

In this paper, the stochastic optimal control problems, which frequently occur in economic and finance are investigated. First, using Bellman’s dynamic programming method the stochastic optimal control problems are converted to Hamilton-Jacobi-Bellman (HJB) equation. Then, obtained HJB equation is solved through the method of separation of variables by guessing a solution via its terminal condition. Also, the non-linear optimal feedback control law is constructed. Finally, the solution procedure is illustrated for solving some examples that two of them are financial models. In fact, to highlight the applications of stochastic optimal control problems in financial mathematics, some financial models are presented.

In this paper, we have introduced efficiency of order m for a class of non-differentiable multi-objective variational problems in which every component of the objective and constraint function contains a term involving the square root of a certain positive semidefinite quadratic form. Necessary optimality conditions are obtained for this solution concept . Parametric dual of non-differentiable multi-objective fractional variational problem is proposed. Duality theorems are proved to relate efficient solutions of order m for primal problem and its dual. These results are obtained using generalized

In this paper, we investigate the subspace transitivity and subspace supercyclicity of tuples of left multiplication operators in the strong operator topology and in the norm of Hilbert-Schmidt operators.

This paper deals with a class of vector semi-infinite optimization problems with differentiable data and arbitrary index set of inequality constraints. A suitable constraint qualification and a new extension of invexity are introduced, and the weak and strong KarushKuhn-Tucker type optimality conditions are investigated

Let T be a weakly compact left multiplier on L∞0 (G) ∗. In this paper, we prove that if T is positive, then T maps L∞0 (G) ∗ into L1(G) and T is of the form φT for some positive function φ ∈ L1(G). Using this result, we show that T = T + − T − for some positive weakly compact left multipliers T +, T − on L∞0 (G) ∗ if and only if T maps L∞0 (G) ∗ into L1(G)

While there have been many number of studies about best approximation in some spaces, there has been little work on pre-Hilbert C∗-modules. Here we provide such a study that leads to a number of approximation theorems. In particular, some results about existence and uniqueness of best approximation of submodules on Hilbert C∗-modules are also presented. This will be done by considering the C∗-algebra valued map x → |x| where |x| = x, x 1 2 . Also we show that when K is a convex subset of a pre- Hilbert C∗-module X; it is a Chebyshev set with respect to C∗-valued norm which is defined on X. In the end, we study various properties of an A-valued metric projection onto a convex set and a submodule

In this paper, we study the ideal amenability of tensor product of Banach algebras. Among other things, we show that the ideal amenability $\mathcal A\widehat{\otimes}\mathcal B$ implies the ideal amenability of Banach algebras $\mathcal A$ and $\mathcal B$ for which character spaces of $\mathcal A$ and $\mathcal B$ are non-empty. Finally, we provide some examples in which $\mathcal A\widehat{\otimes}\mathcal B$ is ideally amenable.