Initial seven coefficient estimates for a subclass of bi-starlike functions

Ключові слова: Analytic functions, Univalent functions, Bi-univalent functions, Bi-starlike,

Анотація

УДК 517.5

Початковi оцiнки семи коефiцiєнтiв для пiдкласу бiзiркових функцiй

Досліджується підклас бізіркових функцій та вперше отримано оцінки сімох початкових коефіцієнтів Тейлора–Маклорена $|a_{2}|, |a_{3}|, \ldots , |a_{7}|$ для функцій у підкласі функціонального класу $\Sigma.$
Також вказано деякі наслідки результатів, як нові, так і відомі раніше.

Посилання

A. K. Bakhtin, G. P. Bakhtina, Yu. B. Zelinskii, Topological-algebraic structures and geometric methods in complex analysis, Proc. Inst. Math. NAS Ukraine, 73 (2008).

A. K. Bakhtin, I. V. Denega, Weakened problem on extremal decomposition of the complex plane, Mat. Stud., 51, № 1, 35 – 40 (2019), https://doi.org/10.15330/ms.51.1.35-40 DOI: https://doi.org/10.15330/ms.51.1.35-40

D. A. Brannan, J. G. Clunie (Eds), Aspects of contemporary complex analysis, Proc. NATO Adv. Study Inst., Univ. Durham, Durham, July, 1979, Acad. Press, New York, London (1980), p. 1 – 20.

D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, Stud. Univ. Babe¸s-Bolyai Math., Some Math. J., 31, № 2, 70 – 77 (1986).

I. Denega, Estimates of the inner radii of non-overlapping domains, J. Math. Sci., № 6, 1 – 9 (2019). DOI: https://doi.org/10.1007/s10958-019-04516-2

I. V. Denega, Ya. V. Zabolotnii, Estimates of products of inner radii of non-overlapping domains in the complex plane, Complex Var. and Elliptic Equat., 62, № 11, 1611 – 1618 (2017)б https://doi.org/10.1080/17476933.2016.1265952 DOI: https://doi.org/10.1080/17476933.2016.1265952

E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal., 2, № 1, 49 – 60 (2013), https://doi.org/10.7153/jca-02-05 DOI: https://doi.org/10.7153/jca-02-05

V. Ya. Gutlyanskii, V. I. Ryazanov, Geometric and topological theory of functions and mappings, Naukova Dumka, Kyiv (2011).

T. Janani, G. Murugusundaramoorthy, K. Vijaya, New subclass of pseudo-type meromorphic bi-univalent functions of complex order, Novi Sad J. Math., 48, № 1, 93 – 102 (2018), https://doi.org/10.30755/nsjom.06870 DOI: https://doi.org/10.30755/NSJOM.06870

M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18, 63 – 68 (1967), https://doi.org/10.2307/2035225 DOI: https://doi.org/10.1090/S0002-9939-1967-0206255-1

G. Murugusundaramoorthy, Subclasses of bi-univalent functions of complex order based on subordination conditions involving wright hypergeometric functions, J. Math. and Fundam. Sci., 47, 60 – 75 (2015), https://doi.org/10.5614/j.math.fund.sci.2015.47.1.5 DOI: https://doi.org/10.5614/j.math.fund.sci.2015.47.1.5

E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in $| z| < 1$, Arch. Ration. Mech. and Anal., 32, 100 – 112 (1969), https://doi.org/10.1007/BF00247676 DOI: https://doi.org/10.1007/BF00247676

Z. Peng, G. Murugusundaramoorthy, T. Janani, Coefficient estimate of bi-univalent functions of complex order associated with the Hohlov operator, J. Complex Anal., 2014, Article 693908, (2014), p. 1 – 6, https://doi.org/10.1155/2014/693908 DOI: https://doi.org/10.1155/2014/693908

H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23, 1188 – 1192 (2010), https://doi.org/10.1016/j.aml.2010.05.009 DOI: https://doi.org/10.1016/j.aml.2010.05.009

T. S. Taha, Topics in univalent function theory, Ph. D. Thesis, Univ. London (1981).

Q.-H. Xu, Y.-C. Gui, H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25, № 6, 990 – 994 (2012), https://doi.org/10.1016/j.aml.2011.11.013 DOI: https://doi.org/10.1016/j.aml.2011.11.013

Q.-H. Xu, H.-G. Xiao, H. M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. and Comput., 218, 11461 – 11465 (2012), https://doi.org/10.1016/j.amc.2012.05.034 DOI: https://doi.org/10.1016/j.amc.2012.05.034

C. Pommerenke, Univalent functions, Vandenhoeck & Ruprecht, G¨ottingen (1975).

W. C. Ma, D. Minda, A unified treatment of some special classes of functions, Proc. Conf. Complex Anal., Tianjin, 1992, Conf. Proc. Lect. Notes Anal., Int. Press, Cambridge, MA (1994), p. 157 – 169.

Опубліковано
23.11.2021
Як цитувати
JananiT., і YalçınS. «Initial Seven Coefficient Estimates for a Subclass of Bi-Starlike Functions». Український математичний журнал, вип. 73, вип. 11, Листопад 2021, с. 1576 -84, doi:10.37863/umzh.v73i11.1046.
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