In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n = 4, 5, we find the constrained Jacobi polynomial, and for n ≥ 6, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

This paper is concerned with the problem of nonlinear simultaneous Chebyshev approximation in a real continuous function space. Some results on existence are established, in addition to characterization conditions of Kolmogorov type and also of alternation type. Applications are given to approximation by rational functions, by exponential sums and by Chebyshev splines with free knots.  2003 El...

This paper concerns the iterative solution of the linear system arising from the Chebyshev–collocation approximation of second-order elliptic equations and presents an optimal multigrid preconditioner based on alternating line Gauss–Seidel smoothers for the corresponding stiffness matrix of bilinear finite elements on the Chebyshev–Gauss–Lobatto grid.  2000 IMACS. Published by Elsevier Science...

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

The usual way to determine the asymptotic behavior of the Chebyshev coefficients for a function is to apply the method of steepest descent to the integral representation of the coefficients. However, the procedure is usually laborious. We prove an asymptotic upper bound on the Chebyshev coefficients for the kth integral of a function. The tightness of this upper bound is then analyzed for the c...

We consider the evaluation of a recent generalization of the Epstein-Hubbell elliptic-type integral using the tau method approximation with a Chebyshev polynomial basis. This also leads to an approximation of Lauricella’s hypergeometric function of three variables. Numerical results are given for polynomial approximations of degree 6.

In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [−1, 1] to arbitrary complex poles outside [−1, 1]. The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrat...

In this note, we characterize Chebyshev subalgebras of unital JB-algebras. We exhibit that if B is Chebyshev subalgebra of a unital JB-algebra A, then either B is a trivial subalgebra of A or A= H R .l, where H is a Hilbert space

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

The theorem proved here extends Chebyshev theory into what has previously been no man's land: functions which have an infinite number of bounded derivatives on the expansion interval [a, b] but which are singular at one endpoint. The Chebyshev series in l/x for all the familiar special functions fall into this category, so this class of functions is very important indeed. In words, the theorem ...