Faber polynomial coefficients for meromorphic bi-subordinate functions of complex order

Erhan Deniz; Hatice Tuǧba Yolcu; Erhan Deniz; Hatice Tuǧba Yolcu

doi:10.3934/math.2020043

AIMS Mathematics

2020, Volume 5, Issue 1: 640-649. doi: 10.3934/math.2020043

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Research article

Faber polynomial coefficients for meromorphic bi-subordinate functions of complex order

Erhan Deniz ^,,
Hatice Tuǧba Yolcu

Department of Mathematics, Faculty of Science and Letters, Kafkas University, 36100, Kars, Turkey

Received: 11 October 2019 Accepted: 16 December 2019 Published: 16 December 2019
MSC : 30C45, 30C80

In this paper, we obtain the upper bounds for the n-th (n ≥ 1) coefficients for meromorphic bi-subordinate functions of complex order by using Faber polynomial expansions. The results, which are presented in this paper, would generalize those in related works of several earlier authors.
- analytic functions,
- starlike functions,
- meromorphic functions,
- bi-univalent functions,
- subordination,
- Faber polynomial
Citation: Erhan Deniz, Hatice Tuǧba Yolcu. Faber polynomial coefficients for meromorphic bi-subordinate functions of complex order[J]. AIMS Mathematics, 2020, 5(1): 640-649. doi: 10.3934/math.2020043

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Abstract

In this paper, we obtain the upper bounds for the n-th (n ≥ 1) coefficients for meromorphic bi-subordinate functions of complex order by using Faber polynomial expansions. The results, which are presented in this paper, would generalize those in related works of several earlier authors.

References

[1]	H. Airault, A. Bouali, Differential calculus on the Faber polynomials, B. Sci. Math., 130 (2006), 179-222. doi: 10.1016/j.bulsci.2005.10.002
[2]	H. Airault, J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, B. Sci. Math., 126 (2002), 343-367. doi: 10.1016/S0007-4497(02)01115-6
[3]	A. Bouali, Faber polynomials, Cayley-Hamilton equation and Newton symmetric functions, B. Sci. Math., 130 (2006), 49-70. doi: 10.1016/j.bulsci.2005.08.002
[4]	S. Bulut, Coefficient estimates for new subclasses of meromorphic bi-univalent functions, Int. Scholarly Res. Notices, 2014 (2014), 376076.
[5]	S. Bulut, N. Magesh, V. K. Balaji, Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions, C. R. Math. Acad. Sci. Paris, 353 (2015), 113-116. doi: 10.1016/j.crma.2014.10.019
[6]	P. L. Duren, Coefficients of meromorphic schlicht functions, P. Am. Math. Soc., 28 (1971), 169-172. doi: 10.1090/S0002-9939-1971-0271329-7
[7]	G. Faber, Uber polynomische Entwickelungen, Math. Ann., 57 (1903), 389-408. doi: 10.1007/BF01444293
[8]	S. A. Halim, S. G. Hamidi, V. Ravichandran, et al. Coefficient estimates for certain classes of meromorphic bi-univalent functions, C. R. Math. Acad. Sci. Paris, 352 (2014), 277-282. doi: 10.1016/j.crma.2014.01.010
[9]	S. G. Hamidi, S. A. Halim, J. M. Jahangiri, Coefficient estimates for a class of meromorphic bi-univalent functions, C. R. Math. Acad. Sci. Paris, 351 (2013), 349-352. doi: 10.1016/j.crma.2013.05.005
[10]	S. G. Hamidi, S. A. Halim, J. M. Jahangiri, Faber polynomial coefficient estimates for meromorphic bi-starlike functions, Int. J. Math. Math. Sci., 2013 (2013), 498159.
[11]	T. Janani, G. Murugusundaramoorthy, Coefficient estimates of meromorphic bi-starlike functions of complex order, Int. J. Anal. Appl., 4 (2014), 68-77.
[12]	G. P. Kapoor, A. K. Mishra, Coefficient estimates for inverses of starlike functions of positive order, J. Math. Anal. Appl., 329 (2007), 922-934. doi: 10.1016/j.jmaa.2006.07.020
[13]	Y. Kubota, Coefficients of meromorphic univalent functions, Kodai Mathematical Seminar Reports, Department of Mathematics, Tokyo Institute of Technology, 28 (1977), 253-261. doi: 10.2996/kmj/1138847445
[14]	A. Motamednezhad, S. Salehian, Faber polynomial coefficient estimates for certain subclass of meromorphic bi-univalent functions, Commun. Korean Math. Soc., 33 (2018), 1229-1237.
[15]	F. M. Sakar, Estimating coefficients for certain subclasses of meromorphic and bi-univalent functions, J. Inequal. Appl., 2018 (2018), 283.
[16]	T. Panigrahi, Coefficient bounds for certain subclasses of meromorphic and bi-univalent functions, B. Korean Math. Soc., 50 (2013), 1531-1538. doi: 10.4134/BKMS.2013.50.5.1531
[17]	C. Pommerenke, Univalent Functions, Gottingen: Vandenhoeck & Ruprecht, 1975.
[18]	M. Schiffer, Sur un problème d'extrémum de la représentation conforme, B. Soc. Math. Fr., 66 (1938), 48-55.
[19]	G. Schober, Coefficients of inverses of meromorphic univalent functions, P. Am. Math. Soc., 67 (1977), 111-116. doi: 10.1090/S0002-9939-1977-0454000-3
[20]	G. Springer, The coefficient problem for schlicht mappings of the exterior of the unit circle, T. Am. Math. Soc., 70 (1951), 421-450. doi: 10.1090/S0002-9947-1951-0041935-5
[21]	P. G. Todorov, On the Faber polynomials of the univalent functions of class, J. Math. Anal. Appl., 162 (1991), 268-276. doi: 10.1016/0022-247X(91)90193-4
[22]	H. G. Xiao, Q. H. Xu, Coefficient estimates for three generalized classes of meromorphic and bi-univalent functions, Filomat, 29 (2015), 1601-1612. doi: 10.2298/FIL1507601X

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