Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
generalized bivariate Fibonacci polynomial; analytic function; bi-univalent function; coefficient estimate; Fekete-Szegö functional; coefficients of inverse function
generalized bivariate Fibonacci polynomial; analytic function; bi-univalent function; coefficient estimate; Fekete-Szegö functional; coefficients of inverse function
Summary:
We introduce a novel subclass of bi-univalent functions with respect to symmetric points using generalized bivariate Fibonacci polynomials. Then we determine certain bounds for the initial coefficients of Maclaurin expansion of the functions belonging to this class of functions. In addition, we study the well-known Fekete-Szegö inequality for defined function class. We also discuss the same problems for the inverses of functions in this subclass. Further, we give a few corollaries for particular parameter values.
References:
[1] Al-Asadi, A. M. A., Al-Ziadi, N. A. J.: Exploring new subclasses of bi-univalent functions using Gegenbauer polynomials: Coefficient bounds and Fekete-Szegö problems. AIP Conf. Proc. 3169 (2025), Article ID 070013. DOI 10.1063/5.0254958
[2] nkaya, Ş. Altı, n, S. Yalçı: Faber polynomial coefficient bounds for a subclass of bi-univalent functions. C. R., Math., Acad. Sci. Paris 353 (2015), 1075-1080. DOI 10.1016/j.crma.2015.09.003 | MR 3427911 | Zbl 1335.30005
[3] nkaya, Ş. Altı, n, S. Yalçı: On the $(p,q)$-Lucas polynomial coefficient bounds of the bi-univalent function class $\sigma$. Bol. Soc. Mat. Mex., III. Ser. 25 (2019), 567-575. DOI 10.1007/s40590-018-0212-z | MR 4022306 | Zbl 1430.30006
[4] nkaya, Ş. Altı, n, S. Yalçı: On the Chebyshev polynomial coefficient problem of bi-Bazilevič function. TWMS J. Appl. Eng. Math. 10 (2020), 251-258.
[5] Amourah, A.: Initial bounds for analytic and bi-univalent functions by means of $(p,q)$-Chebyshev polynomials defined by differential operator. Gen. Lett. Math. 7 (2019), 45-51. DOI 10.31559/glm2019.7.2.1
[6] Amourah, A.: Fekete-Szegö inequality for analytic and bi-univalent functions subordinate to $(p,q)$-Lucas polynomials. TWMS J. Appl. Eng. Math. 11 (2021), 959-965.
[7] Amourah, A., Frasin, B. A., Murugusundaramoorthy, G., Al-Hawary, T.: Bi-Bazilevič functions of order $ \nu+i\delta$ associated with $(p,q)$-Lucas polynomials. AIMS Math. 6 (2021), 4296-4305. DOI 10.3934/math.2021254 | MR 4220409 | Zbl 1484.30005
[8] Brannan, D. A., (Eds.), J. G. Clunie: Aspects of Contemporary Complex Analysis. Academic Press, New York (1980). MR 0623462 | Zbl 0483.00007
[9] Brannan, D. A., Taha, T. S.: On some classes of bi-univalent functions. Mathematical Analysis and its Applications KFAS Proceedings Series 3. Pergamon Press, Oxford (1988), 53-60. DOI 10.1016/B978-0-08-031636-9.50012-7 | MR 0951657 | Zbl 0703.30014
[10] Bulut, S., Magesh, N., Balaji, V. K.: Initial bounds for analytic and bi-univalent functions by means of Chebyshev polynomials. J. Class. Anal. 11 (2017), 83-89. DOI 10.7153/jca-11-06 | MR 3671180 | Zbl 1424.30033
[11] Das, R. N., Singh, P.: On subclasses of schlicht mappings. Indian J. Pure Appl. Math. 8 (1977), 864-872. MR 0486470 | Zbl 0374.30008
[12] Duren, P. L.: Univalent Functions. Grundlehren der Mathematischen Wissenschaften 259. Springer, New York (1983). MR 0708494 | Zbl 0514.30001
[13] Frasin, B. A., Swamy, S. R., Aldawish, I.: A comprehensive family of biunivalent functions defined by $k$-Fibonacci numbers. J. Funct. Spaces 2021 (2021), Article ID 4249509, 7 pages. DOI 10.1155/2021/4249509 | MR 4335587 | Zbl 1482.30034
[14] Frasin, B. A., Swamy, S. R., Nirmala, J.: Some special families of holomorphic and Al-Oboudi type bi-univalent functions related to $k$-Fibonacci numbers involving modified Sigmoid activation function. Afr. Mat. 32 (2021), 631-643. DOI 10.1007/s13370-020-00850-w | MR 4259360 | Zbl 1488.30069
[15] Gbolagade, A. M., Awolere, I. T., Adeyemo, O., Oladipo, A. T.: Application of the neutrosophic Poisson distribution series on the harmonic subclass of analytic functions using the Salagean derivative operator. Neutrosophic Syst. Appl. 23 (2024), 33-46. DOI 10.61356/j.nswa.2024.23390
[16] Güney, H. Ã., Murugusundaramoorthy, G., Sokół, J.: Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers. Acta Univ. Sapientiae, Math. 10 (2018), 70-84. DOI 10.2478/ausm-2018-0006 | MR 3854091 | Zbl 1412.30043
[17] Güney, H. Ã., Murugusundaramoorthy, G., Sokół, J.: Certain subclasses of bi-univalent functions related to $k$-Fibonacci numbers. Commun. Fac. Sci. Univ. Ank., Sér. A1., Math. Stat. 68 (2019), 1909-1921. DOI 10.31801/cfsuasmas.505287 | MR 4010330 | Zbl 1494.30026
[18] Hamidi, S. G., Jahangiri, J. M.: Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations. Bull. Iran. Math. Soc. 41 (2015), 1103-1119. MR 3416618 | Zbl 1373.30019
[19] Hohlov, J. E.: Operators and operations on the class of univalent functions. Izv. Vyssh. Uchebn. Zaved., Mat. 10 (1978), 83-89 Russian. MR 0522766 | Zbl 0406.30009
[20] Hu, Q., Shaba, T. G., Younis, J., Khan, B., Mashwani, W. K., Çağlar, M.: Applications of $q$-derivative operator to subclasses of bi-univalent functions involving Gegenbauer polynomials. Appl. Math. Sci. Eng. 30 (2022), 501-520. DOI 10.1080/27690911.2022.2088743 | MR 4442844
[21] Kocer, E. G., Tuncez, S.: Bivariate Fibonacci and Lucas like polynomials. Gazi Univ. J. Sci. 29 (2016), 109-113.
[22] Lewin, M.: On a coefficient problem for bi-univalent functions. Proc. Am. Math. Soc. 18 (1967), 63-68. DOI 10.1090/S0002-9939-1967-0206255-1 | MR 0206255 | Zbl 0158.07802
[23] Miller, S. S., Mocanu, P. T.: Differential Subordinations: Theory and Applications. Pure and Applied Mathematics, Marcel Dekker 225. Marcel Dekker, New York (2000). DOI 10.1201/9781482289817 | MR 1760285 | Zbl 0954.34003
[24] 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. DOI 10.1007/BF00247676 | MR 0235110 | Zbl 0186.39703
[25] Noor, K. I., Noor, M. A.: On integral operators. J. Math. Anal. Appl. 238 (1999), 341-352. DOI 10.1006/jmaa.1999.6501 | MR 1715487 | Zbl 0934.30007
[26] Orhan, H., Aktaş, İ., kan, H. Arı: On new subclasses of biunivalent functions associated with the $(p,q)$-Lucas polynomials and bi-Bazilevič type functions of order $\rho+i\xi$. Turk. J. Math. 47 (2023), 98-109. DOI 10.55730/1300-0098.3348 | MR 4556516 | Zbl 1506.30005
[27] Sakaguchi, K.: On a certain univalent mapping. J. Math. Soc. Japan 11 (1959), 72-75. DOI 10.2969/jmsj/01110072 | MR 0107005 | Zbl 0085.29602
[28] Sălăgean, G. S.: Subclasses of univalent functions. Complex Analysis: Fifth Romanian-Finnish Seminar. Part 1 Lecture Notes in Mathematics 1013. Springer, Berlin (1983), 362-372. DOI 10.1007/BFb0066543 | MR 0738107 | Zbl 0531.30009
[29] Saravanan, G., Baskaran, S., Vanithakumari, B., Bulut, S.: Sakaguchi type functions defined by balancing polynomials. Math. Bohem. 150 (2025), 71-83. DOI 10.21136/MB.2024.0173-23 | MR 4869943 | Zbl 08063798
[30] Srivastava, H. M., nkaya, Ş. Altı, n, S. Yalçı: Certain subclasses of bi-univalent functions associated with the Horadam polynomials. Iran. J. Sci. Technol., Trans. A Sci. 43 (2019), 1873-1879. DOI 10.1007/s40995-018-0647-0 | MR 3978601
[31] Srivastava, H. M., Mishra, A. K., Gochhayat, P.: Certain subclasses of analytic and bi-univalent functions. Appl. Math. Lett. 23 (2010), 1188-1192. DOI 10.1016/j.aml.2010.05.009 | MR 2665593 | Zbl 1201.30020
[32] Srivastava, H. M., Motamednezhad, A., Adegani, E. A.: Faber polynomial coefficient estimates for bi-univalent functions defined by using differential subordination and a certain fractional derivative operator. Mathematics 8 (2020), Article ID 172, 12 pages. DOI 10.3390/math8020172
[33] Srivastava, H. M., Murugusundaramoorthy, G., Magesh, N.: Certain subclasses of bi-univalent functions associated with the Hohlov operator. Global J. Math. Anal. 1 (2013), 67-73.
[34] Srivastava, H. M., Wanas, A. K., Murugusundaramoorthy, G.: A certain family of bi-univalent functions associated with the Pascal distribution series based upon the Horadam polynomials. Surv. Math. Appl. 16 (2021), 193-205. MR 4224411 | Zbl 1470.30017
[35] Srivastava, H. M., Wanas, A. K., Srivastava, R.: Applications of the $q$-Srivastava-Attiya operator involving a certain family of bi-univalent functions associated with the Horadam polynomials. Symmetry 13 (2021), Article ID 1230, 14 pages. DOI 10.3390/sym13071230
[36] Wanas, A. K., Swamy, S. R.: Applications of the second kind Chebyshev polynomials of bi-starlike and bi-convex $\lambda$-pseudo functions associated with Sakaguchi type functions. Earthline J. Math. Sci. 13 (2023), 497-507. DOI 10.34198/ejms.13223.497507
[37] Yilmaz, N., Aktaş, İ.: On some new subclasses of bi-univalent functions defined by generalized bivariate Fibonacci polynomial. Afr. Mat. 33 (2022), Article ID 59, 12 pages. DOI 10.1007/s13370-022-00993-y | MR 4417363 | Zbl 1542.30012
Search
Partner of
