Differential calculus on the Faber polynomials

By H. Airault, Abdlilah Bouali. 2006

122 citations recorded by the source corpus.

Abstract The Faber polynomials are presented as a coordinate system to study the geometry of the manifold of coefficients of univalent functions.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bec3b0bca896b195d0ff98f5c501ca1dcb44c2c3

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In Applied Mathematics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions (2014, background): “}, an expansion of K p n is as, [1], K p n = pan + p(p − 1) 2 D 2 n + p! (p − 3)!3! D 3 n + · · · + p! (p − n)!n! D n n, (3.”
Coefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions (2015, background): “In general, an expansion of K n is given by (see, for details, [1]) K n = pan + p(p − 1) 2 D(2)n + p! (p − 3)!3! 3 n + · · · + p! (p − n)!n! n n (p ∈ Z)”
Faber polynomial coefficient estimates for analytic bi-close-to-convex functions (2014, background): “Using the Faber polynomial expansion of functions f ∈ S of the form (1.1), the coeﬃcients of its inverse map F = f − 1 may be expressed as (e. . see [3, Eq (1.33), page 185]): where V j is a homogeneous polynomial in the variables a 2 , a 3 ,... , a n (see [4] and [3]).”
Faber polynomial coefficient bounds for a subclass of bi-univalent functions (2015, background): “In general, for any p ∈ N, an expansion of K n is as, [3], K n = pan + p (p− 1) 2 E(2) n + p! (p− 3)!3! E(3) n + .”
Faber Polynomial Coefficient Estimates for Bi-univalent Functions Defined by the Tremblay Fractional Derivative Operator (2018, unknown): “1), the coefficients of its inverse map g = f −1 may be expressed (see [1,2]) by g(w) = f −1(w) = w + ∞ ∑ n=2 1 n K−n n−1 (a2, a3, .”
Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator (2020, methodology): “If we make use of the Faber polynomial expansion of functions f ∈ S of the form given by (1), the Taylor-Maclaurin coefficients of its inverse map g = f−1 are expressible as follows (see, for details, [37,38]): g(w) = f−1(w) = w + ∞ ∑ n=2 1 n K−n n−1(a2, a3, · · · , an)w n, (3)”
The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator (2018, background): “In general, for any p ∈ N and n = 2, we have the following expansion of K n(k1, k2, · · · , kn,M) (see [3] and [4]): K n(k1, k2, · · · , kn,M) = p! (p− n)!n! k 1M + p! (p− n+ 1)!(n− 2)! kn−2 1 k2M”