in this paper, a new numerical method is presented for solvingthe optimal control problems of bang-bang type with free or xed terminaltime. the method is based on bezier polynomials which are presented inany interval as [t0; tf ]. the problems are reduced to a constrained problemswhich can be solved by using lagrangian method. the constraints ofthese problems are terminal state and conditions....

In this paper, we consider the problem of best approximation in e,(n), 1 5 p 5 co. If h,, 1 5 p < co, denotes the best &-approximation of the element h E W " from a proper affine subspace K of W " , h @ K, then limp,1 h p-h* where h; is a best er-approximation of h from K, the i, so-called natural best er-approximation. We prove that, for every T E A, the best &approximations have a Taylor expa...

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...

In this work we deal with best approximation in `p , 1 < p ≤ ∞, n ≥ 2. For 1 < p < ∞, let hp denote the best `p -approximation to f ∈ R from a closed, convex subset K of R, f 6∈ K, and let h∗ be a best uniform approximation to f from K. In case that h∗ − f = (ρ1, ρ2, · · · , ρn), |ρj | = ρ for j = 1, 2, · · · , n, we show that the behavior of ‖hp − h∗‖ as p→∞ depends on a property of separation...