A method of constructing a Chebyshev approximation multivariable functions by generalized polynomial with the exact reproduction its values at given points is proposed. It based on sequential construction mean-power approximations, taking into account interpolation condition. The calculated using an iterative scheme least squares variable weight function. An algorithm for calculating parameters...

Several authors have examined connections among restricted permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for involutions which avoid 3412. Our results include a recursive procedure for computing the generating function for involutions which avoid 3412 and any set of additional patterns. We use our results to gi...

In this paper, we obtain initial coefficient bounds for functions belong to a comprehensive subclass of univalent functions by using the Chebyshev polynomials and also we find Fekete-Szegö inequalities for this class. All results are sharp.