Faber Polynomials Corresponding to Rational Exterior Mapping Functions

Faber Polynomials for Rational Mapping Functions

Coefficient Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials

In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

The Faber Polynomials for Circular Sectors

The Faber polynomials for a region of the complex plane, which are of interest as a basis for polynomial approximation of analytic functions, are determined by a conformai mapping of the complement of that region to the complement of the unit disc. We derive this conformai mapping for a circular sector {;: \z\ < 1, |argz| < i/a}, where a > 1, and obtain a recurrence relation for the coefficient...

Boundary Singularities of Faber and Fourier Series

Given an analytic Jordan curve with interior G and exterior and given a sequence of complex numbers fang n satisfying lim sup n janj n we consider here three series of the form f z X n anPn z where the polynomials Pn z are chosen to be i the Faber polynomials associated with G ii the polynomials orthogonal over the area of G and iii the polynomials orthogonal over the contour Here we study the ...

On Approximation to Analytic Functions by Rational Functions

Let f(z) be analytic in the interior of a rectifiable Jordan curve C and continuous in the corresponding closed region C. The relation between continuity properties of f(z) on C and degree of approximarion to f(z) by polynomials irn(z) in z of respective degrees n, n = 1, 2, • • • , has been extensively studied. In the present paper we study the relation between continuity properties of f(z) on...