Results 41 to 50 of about 536,183 (317)
A class of univalent functions [PDF]
Proceedings of the American Mathematical Society, 1964 f'(0)= 1. In this paper we study the subclass denoted by F and defined by the condition If'(z) - Ij < 1 for I zj < 1.
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Nonvanishing univalent functions [PDF]
Mathematische Zeitschrift, 1980 The class S of functions g(z) = z + c 2 z 2 + c 3 z 3 + ... analytic and univalent in the unit disk Izr < 1 has been thoroughly studied, and its properties are well known. Our purpose is to investigate another class of functions which, by contrast, seems to have been rather neglected. This is the class S o of functions f ( z ) = 1 + a 1 z + a 2 z Z + .
Duren, Peter L., Schober, Glenn
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On the asymptotic Bieberbach conjecture
International Journal of Mathematics and Mathematical Sciences, 1982 The set S consists of complex functions f, univalent in the open unit disk, with f(0)=f'(0)-1=0. We use the asymptotic behavior of the positive semidefinite FitzGerald matrix to show that there is an absolute constant N0 such that, for any f(z)=z+?n ...
Mauriso Alves, Armando J. P. Cavalcante
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Schwarzian Derivatives and Uniform Local Univalence
, 2007 Quantitative estimates are obtained for the (finite) valence of functions analytic in the unit disk with Schwarzian derivative that is bounded or of slow growth. A harmonic mapping is shown to be uniformly locally univalent with respect to the hyperbolic
Chuaqui, Martin +2 more
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On a class of univalent functions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2000 We consider the class of univalent functions f(z) = z + a3z3 + a4z4 + ⋯ analytic in the unit disc and satisfying |(z2f′(z)/f2(z)) − 1 | < 1, and show that such functions are starlike if they satisfy .
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On the coefficient domains of univalent functions
International Journal of Mathematics and Mathematical Sciences, 1990 Coefficient domains for functions whose derivative has positive real part in the interior of an ellipse are given in this paper.
M. M. Elhosh
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On the logarithmic coefficients for some classes defined by subordination
AIMS Mathematics, 2023 The logarithmic coefficients of univalent functions play an important role in different estimates in the theory of univalent functions. In this paper, due to the significant importance of the study of these coefficients, we find the upper bounds for some
Ebrahim Analouei Adegani +4 more
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Univalence of Bessel functions [PDF]
Proceedings of the American Mathematical Society, 1960 In particular we shall first determine a radius of univalence for the normalized Bessel functions [J,(z) ]1Iv for values of v belonging to the region G defined by the inequalities (i v} >0, I arg v|
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Prawitz's area theorem and univalence criterion [PDF]
arXiv, 2023 In this note we investigate the Prawitz's area theorem and establish a new univalence criterion for the locally univalent analytic functions in the unit disk, which generalizes some related results of Aharonov [Duke Math. J., 36(1969), 599-604].
arxiv
Applications of Theory of Differential Subordination for Functions with Fixed Initial Coefficient to Univalent Functions [PDF]
Annales Polonici Mathematici, 105 (2012), 225-238, 2012 By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions is evident in the results obtained.
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