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Univalency of Certain Transform of Univalent Functions
Proceedings of the Bulgarian Academy of Sciences, 2023 We consider univalency problem in the unit disc $$\mathbb{D}$$ of the function \[g(z)=\frac{(z/f(z))-1}{-a_{2}}, \] where $$f$$ belongs to some classes of univalent functions in $$\mathbb{D}$$ and $$a_{2}=\frac{f''(0)}{2}\neq 0$$.
Obradović, Milutin, Tuneski, Nikola
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Univalent harmonic functions [PDF]
Transactions of the American Mathematical Society, 1987 Several families of complex-valued, univalent, harmonic functions are studied from the point of view of geometric function theory. One class consists of mappings of a simply-connected domain onto an infinite horizontal strip with a normalization at the origin.
Hengartner, W., Schober, G.
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Univalence Criteria for Locally Univalent Analytic Functions
Ukrainian Mathematical Journal, 2023 UDC 517.5 Suppose that p ( z ) = 1 + z ϕ ' ' ( z ) / ϕ ' ( z ) , where ϕ ( z ) is a locally univalent analytic function in the unit disk D with ϕ ( 0 ) = ϕ ' ( 1 ) - 1 = 0. We establish the lower and upper bounds for the best constants σ 0
Hu, Zhenyong +2 more
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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–
Pascu, Mihai N., Pascu, Nicolae R.
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Nonvanishing univalent functions III
Annales Academiae Scientiarum Fennicae. Series A. I. Mathematica, 1985 In two previous papers [Math. Z. 170, 195-216 (1980; Zbl 0411.30010) and Ann. Univ. Mariae Curie-Skłodowska, Sect. A 36/37 (1982-83), 33-43 (1983; Zbl 0572.30020)] we studied the class \(S_ 0\) of functions f analytic, univalent, and nonvanishing in the unit disk D, with \(f(0)=1\).
Duren, Peter L. (1935- ) +1 more
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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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Nonvanishing Meromorphic Univalent Functions [PDF]
Proceedings of the American Mathematical Society, 1988 This note studies the best constants s s such that the function k ( z ) = z + 2 + 1 / z k(z) = z + 2 + 1/z solves the linear coefficient problems max Re { s
Abu-Muhanna, Yusuf, Schober, Glenn
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Quasi‐convex univalent functions [PDF]
International Journal of Mathematics and Mathematical Sciences, 1979 In this paper, a new class of normalized univalent functions is introduced. The properties of this class and its relationship with some other subclasses of univalent functions are studied. The functions in this class are close‐to‐convex.
K. Inayat Noor, D. K. Thomas
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Subordination by Univalent Functions [PDF]
Proceedings of the American Mathematical Society, 1981 Let K K be the class of functions f ( z ) = z + a 2 z 2 + ⋯ f(z) = z + {a_2}{z^2} + \cdots , which are regular and univalently convex in
Singh, Sunder, Singh, Ram
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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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