An algebra of differential operators and generating functions on the set of univalent functions

By H. Airault, Jiagang Ren. 2002

102 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ac5ab30c84b09fa63ca8ea081342d70f0768089b

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In Geometry and Topology

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Citations in the corpus

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 a comprehensive subclass of analytic bi-univalent functions (2014, unknown): “,an [3].”
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 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)”
Coefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions (2015, background): “3) and V j (7 5 j 5 n) is a homogeneous polynomial in the variables a2, a3, · · · , an (see, for details, [2]).”
Differential calculus on the Faber polynomials (2006, methodology): “We show how the methods introduced in [2] and [3] allow to do differential calculus on the manifold of coefficients of univalent functions.”
Faber polynomial coefficient bounds for a subclass of bi-univalent functions (2015, unknown): “, an [4].”