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Univalent functions having univalent derivatives [PDF]
Rocky Mountain Journal of Mathematics, 1986 Let T denote the family of functions \(f(z)=z-\sum^{\infty}_{n=2}a_ nz^ n\), \(a_ n\geq 0\), which are analytic and univalent in the unit disk \(\Delta =\{| z|
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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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NEIGHBOURHOODS OF UNIVALENT FUNCTIONS [PDF]
Bulletin of the Australian Mathematical Society, 2010 AbstractThe main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro–
Nicolae R. Pascu, Mihai N. Pascu
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On a class of univalent functions
Applied Mathematics Letters, 2012 AbstractLet A be the class of analytic functions in the unit disk D with the normalization f(0)=f′(0)−1=0. Denote by N the class of functions f∈A which satisfy the condition |−z3(zf(z))‴+f′(z)(zf(z))2−1|≤1,z∈D. We show that functions in N are univalent in D but not necessarily starlike.
Obradović, Milutin +1 more
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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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On a class of univalent functions [PDF]
International Journal of Mathematics and Mathematical Sciences, 1999 We consider the class of univalent functions defined by the conditions f(z)/z ≠ 0 and |(z/f(z))′′| ≤ α, |z| < 1, where f(z) = z + ⋯ is analytic in |z| < 1 and 0 < α ≤ 2.
Dinggong Yang, Jin-Lin Liu
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On the Univalence of Poly-analytic Functions [PDF]
Computational Methods and Function Theory, 2021 A continuous complex-valued function $F$ in a domain $D\subseteq\mathbf{C}$ is Poly-analytic of order $ $ if it satisfies $\partial^ _{\overline{z}}F=0.$ One can show that $F$ has the form $F(z)={\displaystyle\sum\limits_{0}^{n-1}}\overline{z}^{k}A_{k}(z)$, where each $A_k$ is an analytic function$.$ In this paper, we prove the existence of a Landau ...
Layan El Hajj, Zayid Abdulhadi
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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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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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A class of univalent functions [PDF]
Hokkaido Mathematical Journal, 1998 Let \(A\) denote the class of normalized analytic functions in the open unit disc \(U\) of the complex plane. Let \(S^*(\beta)\) denote functions in \(A\) which are starlike of order \(\beta\) and \(S^*= S^*(0)\). In this paper, the author investigates conditions on \(f\in A\) so that \(f\in S^*(\beta)\).
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