| Title:
|
Initial coefficients for generalized subclasses of bi-univalent functions defined with subordination (English) |
| Author:
|
Singh, Gagandeep |
| Author:
|
Singh, Gurcharanjit |
| Author:
|
Singh, Gurmeet |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2022 |
| Pages:
|
105-113 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is concerned with certain generalized subclasses of bi-univalent functions defined with subordination in the open unit disc $E=\left\rbrace z:\mid z \mid <1\right\lbrace $. The bounds for the initial coefficients for the functions in these classes are studied. The earlier known results follow as special cases. (English) |
| Keyword:
|
coefficient estimates |
| Keyword:
|
analytic functions |
| Keyword:
|
univalent functions |
| Keyword:
|
bi-univalent functions |
| Keyword:
|
generalized Sãlãgean operator |
| Keyword:
|
subordination |
| MSC:
|
30C45 |
| MSC:
|
30C50 |
| idZBL:
|
Zbl 07547204 |
| idMR:
|
MR4448486 |
| DOI:
|
10.5817/AM2022-2-105 |
| . |
| Date available:
|
2022-05-16T10:32:10Z |
| Last updated:
|
2022-08-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150424 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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[3] Aouf, M.K.: On a class of $p$-valent starlike functions of order $\alpha $.Int. J. Math. Math. Sci. 10 (4) (1987), 733–744. MR 0907789, 10.1155/S0161171287000838 |
| Reference:
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[4] Brannan, D.A., Taha, T.S.: On some classes of bi-univalent functions.Mathematical Analysis and its Applications, Kuwait, February 18–21, 1985 (Mazhar, S.M., Hamoni, A., Faour, N.S., eds.), KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 53–60, 1985, See also Studia Univ. Babes-Bolyai Math., 1986, 31(2), 70–77. MR 0951657 |
| Reference:
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| Reference:
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[6] Joshi, S., Altinkya, S., Yalcin, S.: Coefficient estimates for Sãlãgean type $\lambda $-bi-pseudo-starlike functions.Kyungpook Math. J. 57 (2017), 613–621. MR 3745142 |
| Reference:
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| Reference:
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[8] Juma, A.R S., Aziz, F.S.: Applying Ruscheweyh derivative on two subclasses of bi-univalent functions.Int. J. Basic Appl. Sci. 12 (6) (2012), 68–74. |
| Reference:
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[9] Lewin, M.: On a coefficient problem for bi-univalent functions.Proc. Amer. Math. Soc. 18 (1967), 63–68. MR 0206255, 10.1090/S0002-9939-1967-0206255-1 |
| Reference:
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[10] Magesh, N., Bulut, S.: Chebyshev polynomial coefficient estimates for a class of analytic bi-univalent functions related to pseudo-starlike functions.Afrika Mat. 29 (2018), 203–209. MR 3761423, 10.1007/s13370-017-0535-3 |
| Reference:
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[11] Magesh, N., Rosy, T., Varma, S.: Coefficient estimate problem for a new subclass of bi-univalent functions.J. Complex Anal. 2013 (2013), 3 pp., Article ID 474231. MR 3124622 |
| Reference:
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[12] Mazi, E.P., Opoola, T.O.: On some subclasses of bi-univalent functions associating pseudo-starlike functions with Sakaguchi type functions.Gen. Math. 25 (2017), 85–95. |
| Reference:
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[14] Singh, Gagandeep: Coefficient estimates for bi-univalent functions with respect to symmetric points.J. Nonlinear Func. Anal. 1 (2013), 1–9, Article ID 2013. |
| Reference:
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[15] Singh, Gurmeet, Singh, Gagandeep, Singh, Gurcharanjit: Certain subclasses of Sakaguchi-type bi-univalent functions.Ganita 69 (2) (2019), 45–55. MR 4060858 |
| Reference:
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[16] Singh, Gurmeet, Singh, Gagandeep, Singh, Gurcharanjit: A generalized subclass of alpha-convex bi-univalent functions of complex order.Jnanabha 50 (1) (2020), 65–71. MR 3962610 |
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[17] Singh, Gurmeet, Singh, Gagandeep, Singh, Gurcharanjit: Certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers.Gen. Math. 28 (1) (2020), 1258–140. MR 3962610 |
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[18] Sivapalan, J., Magesh, N., Murthy, S.: Coefficient estimates for bi-univalent functions with respect to symmetric conjugate points associated with Horadam Polynomials.Malaya J. Mat. 8 (2) (2020), 565–569. MR 4112566, 10.26637/MJM0802/0042 |
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