Here we are concerned with the best approximation by polynomials to rational functions in the uniform norm. We give some new theorems about the best approximation of 1/(1 + x) and 1/(x − a) where a > 1. Finally we extend this problem to that of computing the best approximation of the Chebyshev expansion in uniform norm and give some results and conjectures about this.  2005 IMACS. Published by...

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.

When an approximant is accurate on interval, it only natural to try extend multi-dimensional domains. In the present article we make use of fact that linear rational barycentric interpolants converge rapidly toward analytic and several-times differentiable functions interpolate them two-dimensional starlike domains parametrized in polar coordinates. radial direction, engage at conformally shift...

Fractional order Chebyshev high pass filters have been designed in this paper for orders (1+α), (2+α) and (3+α), α representing the fractional component. The work has done by using nature-inspired evolutionary metaheuristic technique called particle swarm optimization. MATLAB simulations these shown with varying from 0.1 to 0.9 at a step of 0.1. attenuation values are compared ideal values. can...

We are concerned with linear and nonlinear multi-term fractional differential equations (FDEs). The shifted Chebyshev operationalmatrix (COM) of fractional derivatives is derived and used together with spectral methods for solving FDEs. Our approach was based on the shifted Chebyshev tau and collocation methods. The proposed algorithms are applied to solve two types of FDEs, linear and nonlinea...

The paper deals with fractional derivative introduced by means of Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the correspondence with some well known approaches is shown. In particular it is shown how the uniqueness of the operation depends on the derivative order type (integer, rat...

This thesis is based on the following paper :Mehdi Dehghan , M.R. Eslahchi, Best uniform polynomialapproximation of some rational functions , Computers andMathematics with Applications ,Best polynomial approximation problem is one of the mostimportant and applicable subjects in the approxi References1. [1] J . C . Mason , D . C . Handscomb , Chebyshevpolynomials ...

In this paper we introduce an algorithm for solving variational inequality problems when the operator is pseudomonotone and point-to-set (therefore not relying on continuity assumptions). Our motivation development of a method optimisation appearing in Chebyshev rational generalised approximation problems, where approximations are constructed as ratios linear forms (linear combinations basis fu...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...