| Title:
|
Sakaguchi type functions defined by Bernoulli polynomials (English) |
| Author:
|
Gunasekar, Saravanan |
| Author:
|
Sudharsanan, Baskaran |
| Author:
|
Bulut, Serap |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
2 |
| Year:
|
2026 |
| Pages:
|
273-289 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, the class of Sakaguchi-type functions defined by Bernoulli polynomials has been introduced as a novel subclass of bi-univalent functions. The bounds for the Fekete-Szegö inequality and the initial coefficients $\vert a_{2}\vert $ and $\vert a_{3}\vert $ have also been estimated. (English) |
| Keyword:
|
analytic function |
| Keyword:
|
bi-univalent function |
| Keyword:
|
Sakaguchi type function |
| Keyword:
|
Bernoulli polynomial |
| MSC:
|
30C45 |
| MSC:
|
30C50 |
| DOI:
|
10.21136/MB.2025.0104-24 |
| . |
| Date available:
|
2026-05-19T08:23:26Z |
| Last updated:
|
2026-05-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153624 |
| . |
| Reference:
|
[1] Alnajar, O., Amourah, A., Salah, J., Darus, M.: Fekete-Szegö functional problem for analytic and bi-univalent functions subordinate to Gegenbauer polynomials.Contemp. Math. 5 (2024), 5731-5742. 10.37256/cm.5420245636 |
| Reference:
|
[2] Amourah, A., Amoush, A. G. Al, Al-Kaseasbeh, M.: Gegenbauer polynomials and bi-univalent functions.Palest. J. Math. 10 (2021), 625-632. Zbl 1492.30031, MR 4345706 |
| Reference:
|
[3] Amourah, A., Frasin, B. A., Seoudy, T. M.: An application of Miller-Ross-type Poisson distribution on certain subclasses of bi-univalent functions subordinate to Gegenbauer polynomials.Mathematics 10 (2022), Article ID 2462, 10 pages. 10.3390/math10142462 |
| Reference:
|
[4] Baskaran, S., Saravanan, G., Vanithakumari, B.: Sakaguchi type function defined by $(p,q)$-fractional operator using Laguerre polynomials.Palest. J. Math. 11 (2022), 41-47. Zbl 1490.30006, MR 4447012 |
| Reference:
|
[5] Baskaran, S., Saravanan, G., Yalçin, S., Vanithakumari, B.: Sakaguchi type function defined by $(p,q)$-derivative operator using Gegenbauer polynomials.Int. J. Nonlinear Anal. Appl. 13 (2022), 2197-2204. 10.22075/ijnaa.2022.25973.3206 |
| Reference:
|
[6] Brannan, D. A., (eds.), J. G. Clunie: Aspects of Contemporary Complex Analysis.Academic Press, London (1980). Zbl 0483.00007, MR 0623462 |
| Reference:
|
[7] Buyankara, M., Çağlar, M., Otîrlă, L.-I.: New subclasses of bi-univalent functions with respect to the symmetric points defined by Bernoulli polynomials.Axioms 11 (2022), 652-661. 10.3390/axioms11110652 |
| Reference:
|
[8] Cătinaş, T.: An iterative modification of Shepard-Bernoulli operator.Result. Math. 69 (2016), 387-395. Zbl 1339.41002, MR 3499569, 10.1007/s00025-015-0498-3 |
| Reference:
|
[9] Dell'Accio, F., Tommaso, F. Di, Nouisser, O., Zerroudi, B.: Increasing the approximation order of the triangular Shepard method.Appl. Numer. Math. 126 (2018), 78-91. Zbl 1380.65028, MR 3743679, 10.1016/j.apnum.2017.12.006 |
| Reference:
|
[10] Frasin, B. A.: Coefficient inequalities for certain classes of Sakaguchi type functions.Int. J. Nonlinear Sci. 10 (2010), 206-211. Zbl 1216.30008, MR 2745244 |
| Reference:
|
[11] lateş, C. Kızı, Tuğlu, N., Çekim, B.: On the $(p,q) $-Chebyshev polynomials and related polynomials.Mathematics 7 (2019), Article ID 136, 12 pages. 10.3390/math7020136 |
| Reference:
|
[12] Lewin, M.: On a coefficient problem for bi-univalent functions.Proc. Am. Math. Soc. 18 (1967), 63-68. Zbl 0158.07802, MR 0206255, 10.1090/S0002-9939-1967-0206255-1 |
| Reference:
|
[13] Loh, J. R., Phang, C.: Numerical solution of Fredholm fractional integro-differential equation with right-sided Caputo's derivative using Bernoulli polynomials operational matrix of fractional derivative.Mediterr. J. Math. 16 (2019), Article ID 28, 25 pages. Zbl 1411.65168, MR 3911141, 10.1007/s00009-019-1300-7 |
| Reference:
|
[14] Machado, J. T., Kiryakova, V., Mainardi, F.: Recent history of fractional calculus.Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 1140-1153. Zbl 1221.26002, MR 2736622, 10.1016/j.cnsns.2010.05.027 |
| Reference:
|
[15] Natalini, P., Bernardini, A.: A generalization of the Bernoulli polynomials.J. Appl. Math. 2003 (2003), 155-163. Zbl 1019.33011, MR 1982355, 10.1155/S1110757X03204101 |
| Reference:
|
[16] Netanyahu, E.: The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in $|z|<1$.Arch. Ration. Mech. Anal. 32 (1969), 100-112. Zbl 0186.39703, MR 0235110, 10.1007/BF00247676 |
| Reference:
|
[17] Owa, S., Sekine, T., Yamakawa, R.: Notes on Sakaguchi functions.Aust. J. Math. Anal. Appl. 3 (2006), Article ID 12, 7 pages. Zbl 1090.30024, MR 2223016 |
| Reference:
|
[18] Owa, S., Sekine, T., Yamakawa, R.: On Sakaguchi type functions.Appl. Math. Comput. 187 (2007), 356-361. Zbl 1113.30018, MR 2323589, 10.1016/j.amc.2006.08.133 |
| Reference:
|
[19] Sahu, P. K., Mallick, B.: Approximate solution of fractional order Lane-Emden type differential equation by orthonormal Bernoulli's polynomials.Int. J. Appl. Comput. Math. 5 (2019), Article ID 89, 9 pages. Zbl 1416.65198, MR 3957059, 10.1007/s40819-019-0677-0 |
| Reference:
|
[20] Sakaguchi, K.: On a certain univalent mapping.J. Math. Soc. Japan 11 (1959), 72-75. Zbl 0085.29602, MR 0107005, 10.2969/jmsj/01110072 |
| Reference:
|
[21] Saravanan, G., Muthunagai, K.: Coefficient estimates and Fekete-Szegö inequality for a subclass of bi-univalent functions defined by symmetric $q$-derivative operator by using Faber polynomial techniques.Periodicals Engineering Natural Sci. 6 (2018), 241-250. 10.21533/pen.v6i1.285 |
| Reference:
|
[22] Vijayalakshmi, S. P., Bulut, S., Sudharsan, T. V.: Vandermonde determinant for a certain Sakaguchi type function in Limaçon domain.Asian-Eur. J. Math. 15 (2022), Article ID 2250212, 9 pages. Zbl 1504.30016, MR 4504278, 10.1142/S1793557122502126 |
| Reference:
|
[23] Xu, Q.-H., Gui, Y.-C., Srivastava, H. M.: Coefficient estimates for a certain subclass of analytic and bi-univalent functions.Appl. Math. Lett. 25 (2012), 990-994. Zbl 1244.30033, MR 2902367, 10.1016/j.aml.2011.11.013 |
| Reference:
|
[24] Xu, Q.-H., Xiao, H.-G., Srivastava, H. M.: A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems.Appl. Math. Comput. 218 (2012), 11461-11465. Zbl 1284.30009, MR 2943990, 10.1016/j.amc.2012.05.034 |
| Reference:
|
[25] n, S. Yalçı, Muthunagai, K., Saravanan, G.: A subclass with bi-univalence involving $(p,q)$-Lucas polynomials and its coefficient bounds.Bol. Soc. Mat. Mex., III. Ser. 26 (2020), 1015-1022. Zbl 1451.30041, MR 4155343, 10.1007/s40590-020-00294-z |
| Reference:
|
[26] Yousef, F., Alroud, S., Illafe, M.: A comprehensive subclass of bi-univalent functions associated with Chebyshev polynomials of the second kind.Bol. Soc. Mat. Mex., III. Ser. 26 (2020), 329-339. Zbl 1435.30070, MR 4110454, 10.1007/s40590-019-00245-3 |
| . |
