Abstract
The purpose of this paper is to study the class of normalized harmonic functions having a derivative with positive real part and the class of harmonic functions with real part greater than some real number α, (0 ≤ α ≤ 1). Sharp estimates for coefficients and distortion theorems are given.
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References
J. Clunie, T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Series A.I., Math. 9 (1984), 3–25.
A.W. Goodman, Univalent functions, Mariner Publ. Comp. 1 (1983), 77–105.
W. Hengartner, G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1–31.
Z.J. Jakubowski, W. Majchrzak and K. Skalska, Harmonic mappings with a positive real part, Materialy XIV Konferencji Szkoleniowej z Teorii Zagadnien Ekstremalnych, Lodz., (1993), 17–24.
M. Öztürk, Harmonic functions with positive real part, and which are typically real, Hacettepe Bulletin of Natural Sciences and Engineering 16 (1995), 79–89.
T. Sheil-Small, Constants for planar harmonic mappings, J. London Math. Soc. 42 no. 2 (1990), 237–248.
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© 2000 Springer Science+Business Media Dordrecht
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Yalçin, S., Öztürk, M., Yamankaradeniz, M. (2000). On Some Subclasses of Harmonic Functions. In: Functional Equations and Inequalities. Mathematics and Its Applications, vol 518. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4341-7_24
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DOI: https://doi.org/10.1007/978-94-011-4341-7_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5869-8
Online ISBN: 978-94-011-4341-7
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