On some extremal problems in classes of holomorphic functions
B. Platynowicz (1980)
Matematički Vesnik
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B. Platynowicz (1980)
Matematički Vesnik
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S. Sivasubramanian, R. Sivakumar, S. Kanas, Seong-A Kim (2015)
Annales Polonici Mathematici
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Let σ denote the class of bi-univalent functions f, that is, both f(z) = z + a₂z² + ⋯ and its inverse are analytic and univalent on the unit disk. We consider the classes of strongly bi-close-to-convex functions of order α and of bi-close-to-convex functions of order β, which turn out to be subclasses of σ. We obtain upper bounds for |a₂| and |a₃| for those classes. Moreover, we verify Brannan and Clunie’s conjecture |a₂| ≤ √2 for some of our classes. In addition, we obtain the Fekete-Szegö...
Adam Lecko (2002)
Annales Polonici Mathematici
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The purpose of this paper is to study the class of univalent analytic functions defined in the right halfplane ℍ and starlike w.r.t. the boundary point at infinity. An analytic characterization of functions in is presented.
Abbas Kareem Wanas, Basem Aref Frasin (2022)
Mathematica Bohemica
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We introduce and study two certain classes of holomorphic and bi-univalent functions associating -pseudo-starlike functions with Sakaguchi-type functions. We determine upper bounds for the Taylor–Maclaurin coefficients and for functions belonging to these classes. Further we point out certain special cases for our results.
B. Bhowmik, S. Ponnusamy (2008)
Annales Polonici Mathematici
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Let denote the open unit disk and f: → ℂ̅ be meromorphic and univalent in with a simple pole at p ∈ (0,1) and satisfying the standard normalization f(0) = f’(0)-1 = 0. Also, assume that f has the expansion , |z-p| < 1-p, and maps onto a domain whose complement with respect to ℂ̅ is a convex set (starlike set with respect to a point w₀ ∈ ℂ, w₀ ≠ 0 resp.). We call such functions concave (meromorphically starlike resp.) univalent functions and denote this class by resp.). We prove...
G. Murugusundaramoorthy, K. Uma (2010)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Making use of the Hurwitz-Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class . In particular, we obtain integral means inequalities for the function belongs to the class in the unit disc.
S. Ponnusamy, P. Vasundhra (2007)
Annales Polonici Mathematici
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For n ≥ 1, let denote the class of all analytic functions f in the unit disk Δ of the form . For Re α < 2 and γ > 0 given, let (γ,α) denote the class of all functions f ∈ satisfying the condition |f’(z) - α f(z)/z + α - 1| ≤ γ, z ∈ Δ. We find sufficient conditions for functions in (γ,α) to be starlike of order β. A generalization of this result along with some convolution results is also obtained.
M. Obradović (1984)
Matematički Vesnik
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M. K. Aouf, R. M. El-Ashwah, A. A. M. Hassan, A. H. Hassan (2013)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper, we obtain Fekete–Szegö inequalities for a generalized class of analytic functions for which (; ; ; ; ; ) lies in a region starlike with respect to and is symmetric with respect to the real axis.
Karl-Joachim Wirths (2004)
Annales Polonici Mathematici
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Let D denote the open unit disc and f:D → ℂ̅ be meromorphic and injective in D. We further assume that f has a simple pole at the point p ∈ (0,1) and an expansion , |z| < p. In particular, we consider f that map D onto a domain whose complement with respect to ℂ̅ is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted by Co(p). It is proved that for p ∈ (0,1) the domain of variability...
Gunasekar Saravanan, Sudharsanan Baskaran, Balasubramaniam Vanithakumari, Serap Bulut (2025)
Mathematica Bohemica
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The class of Sakaguchi type functions defined by balancing polynomials has been introduced as a novel subclass of bi-univalent functions. The bounds for the Fekete-Szegö inequality and the initial coefficients and have also been estimated.
S. Owa, C. Y. Shen (1988)
Matematički Vesnik
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Albert E. Livingston (1997)
Annales Polonici Mathematici
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Let a < 0 < b and Ω(a,b) = ℂ - ((-∞, a] ∪ [b,+∞)) and U= z: |z| < 1. We consider the class of functions f which are univalent, harmonic and sense-preserving with f(U) = Ω and satisfying f(0) = 0, and .
Saminathan Ponnusamy, Allu Vasudevarao (2010)
Annales Polonici Mathematici
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For γ ∈ ℂ such that |γ| < π/2 and 0 ≤ β < 1, let denote the class of all analytic functions P in the unit disk with P(0) = 1 and in . For any fixed z₀ ∈ and λ ∈ ̅, we shall determine the region of variability for when P ranges over the class As a consequence, we present the region of variability for some subclasses of univalent functions. We also graphically illustrate the region of variability for several sets of parameters.
Ian Graham, Hidetaka Hamada, Gabriela Kohr, Mirela Kohr (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In this paper we consider non-normalized univalent subordination chains and the connection with the Loewner differential equation on the unit ball in . To this end, we study the most general form of the initial value problem for the transition mapping, and prove the existence and uniqueness of solutions. Also we introduce the notion of generalized spirallikeness with respect to a measurable matrix-valued mapping, and investigate this notion from the point of view of non-normalized univalent...
Jacek Dziok (2013)
Annales Polonici Mathematici
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We consider functions of the type , where are real numbers and are -strongly close-to-starlike functions of order . We look for conditions on the center and radius of the disk (a,r) = z:|z-a| < r, |a| < r ≤ 1 - |a|, ensuring that F((a,r)) is a domain starlike with respect to the origin.
H. E. Darwish, A. Y. Lashin, S. M. Sowileh (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In the present work, we introduce the subclass , of starlike functions with respect to -symmetric points of complex order () in the open unit disc . Some interesting subordination criteria, inclusion relations and the integral representation for functions belonging to this class are provided. The results obtained generalize some known results, and some other new results are obtained.