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Relevant bibliographies by topics / General theory of univalent and multivalent functions

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Academic literature on the topic 'General theory of univalent and multivalent functions'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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Journal articles on the topic "General theory of univalent and multivalent functions"

1

Lyzzaik, Abdallah. "The Multivalent Class of Geometrically Close-to-Convex Functions." Canadian Journal of Mathematics 39, no. 2 (1987): 297–308. http://dx.doi.org/10.4153/cjm-1987-013-0.

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The class of univalent close-to-convex functions, K, was introduced by Kaplan [4] and first studied by him. The first important extension to the class of multivalent close-to-convex functions, K(p) where p is a positive integer, was considered by Livingston [7]. Somewhat later, Styer [15] introduced the more general class, Kw(p), of weakly close-to-convex functions by simply taking the closure of Livingston's class K(p) in the topology of locally uniform convergence in B = {z: |z| ≤ 1}.In 1936 Biernacki [2] introduced his class of linearly accessible functions. A function f is linearly accessi

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2

Abu-Muhanna, Y., and A. Lyzzaik. "A geometric criterion for decomposition and multivalence." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 3 (1988): 487–95. http://dx.doi.org/10.1017/s0305004100065099.

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AbstractWe give a quite general geometric criterion for a function analytic in the unit disc to be a polynomial of a univalent function, and hence a criterion for multivalence. We believe that this is the essence why multivalent close-to-convex functions enjoy the latter decomposition property. As another application, we study, as suggested by T. Sheil-Small ‘9’, the geometry of classes of analytic functions which arise from his recent investigation of multivalent harmonic mappings.

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3

Ahuja, O. P., and A. Çetinkaya. "Connecting quantum calculus and harmonic starlike functions." Filomat 34, no. 5 (2020): 1431–41. http://dx.doi.org/10.2298/fil2005431a.

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Quantum calculus or q-calculus plays an important role in hypergeometric series, quantum physics, operator theory, approximation theory, sobolev spaces, geometric functions theory and others. But role of q-calculus in the theory of harmonic univalent functions is quite new. In this paper, we make an attempt to connect quantum calculus and harmonic univalent starlike functions. In particular, we introduce and investigate the properties of q-harmonic functions and q-harmonic starlike functions of order ?.

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4

Li, Jian-Lin, and H. M. Srivastava. "Some Questions and Conjectures in the Theory of Univalent Functions." Rocky Mountain Journal of Mathematics 28, no. 3 (1998): 1035–41. http://dx.doi.org/10.1216/rmjm/1181071753.

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5

Ma, Wancang, and David Minda. "Hyperbolic linear invariance and hyperbolic k-convexity." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 58, no. 1 (1995): 73–93. http://dx.doi.org/10.1017/s1446788700038118.

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AbstractPommerenke initiated the study of linearly invariant families of locally schlicht holomorphic functions defined on the unit disk The concept of linear invariance has proved fruitful in geometric function theory. One aspect of Pommerenke's work is the extension of certain results from classical univalent function theory to linearly invariant functions. We propose a definition of a related concept that we call hyperbolic linear invariance for locally schlicht holomorphic functions that map the unit disk into itself. We obtain results for hyperbolic linearly invariant functions which gene

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6

Pavlović, M., and José Ángel Peláez. "Remarks on the area theorem in the theory of univalent functions." Proceedings of the American Mathematical Society 139, no. 03 (2011): 909. http://dx.doi.org/10.1090/s0002-9939-2010-10333-7.

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7

Nunokawa, Mamoru, and Janusz Sokół. "On Bazilevic functions and Umezawa’s lemma." Filomat 33, no. 6 (2019): 1575–82. http://dx.doi.org/10.2298/fil1906575n.

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We consider some properties on |z| = r < 1 of analytic functions in the unit disk |z| < 1. Applying Umezawa?s lemma, On the theory of univalent functions, Tohoku Math J. 7(1955) 212-228, we prove some suffcient conditions for functions to be in the class of Bazilevic functions and some related results.

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8

Shiba, M. "Conformal mapping of Riemann surfaces and the classical theory of univalent functions." Publications de l'Institut Mathematique 75, no. 89 (2004): 217–32. http://dx.doi.org/10.2298/pim0475217s.

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9

Dubinin, V. N., and E. V. Kostyuchenko. "The Teichmüller extremal problem and distortion theorems in the theory of univalent functions." Siberian Mathematical Journal 40, no. 2 (1999): 258–61. http://dx.doi.org/10.1007/s11202-999-0006-7.

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10

Hidalgo, Rubén A., Irina Markina, and Alexander Vasil'ev. "Finite Dimensional Grading of the Virasoro Algebra." gmj 14, no. 3 (2007): 419–34. http://dx.doi.org/10.1515/gmj.2007.419.

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Abstract The Virasoro algebra is a central extension of the Witt algebra, the complexified Lie algebra of the sense preserving diffeomorphism group of the circle Diff 𝑆1. It appears in Quantum Field Theories as an infinite dimensional algebra generated by the coefficients of the Laurent expansion of the analytic component of the momentum-energy tensor, Virasoro generators. The background for the construction of the theory of unitary representations of Diff 𝑆1 is found in the study of Kirillov's manifold Diff 𝑆1=𝑆1. It possesses a natural Kählerian embedding into the universal Teichmüller space

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Dissertations / Theses on the topic "General theory of univalent and multivalent functions"

1

Latha, S. "Some studies in the theory of univalent and multivalent functions." Thesis, 1994. http://hdl.handle.net/2009/1415.

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Books on the topic "General theory of univalent and multivalent functions"

1

Simon, Barry. Advanced complex analysis. American Mathematical Society, 2015.

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2

1941-, Hag Kari, and Broch Ole Jacob, eds. The ubiquitous quasidisk. American Mathematical Society, 2012.

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