Symmetry and Uniform Approximation by Analytic Functions

Approximation of Analytic Functions by Chebyshev Functions

and Applied Analysis 3 where we refer to 1.4 for the am’s and we follow the convention ∏m−1 j m · · · 1. We can easily check that cm’s satisfy the following relation: m 2 m 1 cm 2 − ( m2 − n2 ) cm am 2.2 for any m ∈ {0, 1, 2, . . .}. Theorem 2.1. Assume that n is a positive integer and the radius of convergence of the power series ∑∞ m 0 amx m is ρ > 0. Let ρ0 min{1, ρ}. Then, every solution y ...

Approximation of Analytic Functions by Special Functions

We survey the recent results concerning the applications of power series method to the study of Hyers–Ulam stability of differential equations.

Approximation of Analytic Functions by Kummer Functions

Rates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions

In this paper, problems related to the approximation of a holomorphic function f on a compact subset E of the complex plane C by rational functions from the class Rn,m of all rational functions of order (n,m) are considered. Let ρn,m = ρn,m( f ; E) be the distance of f in the uniform metric on E from the class Rn,m . We obtain results characterizing the rate of convergence to zero of the sequen...

Approximation by Bounded Analytic Functions: Uniform Convergence as Implied by Mean Convergence^) By

In three recent notes [1], [2], [3] I have discussed uniform convergence by polynomials (in the complex variable) to a given function as a consequence of convergence in the mean of those polynomials to the given function, and also convergence in the mean of one order as a consequence of convergence in the mean of a lower order. The present note contains analogs of those results, but now for app...