Using the (p, q)-derivative operator we introduce new subclasses of analytic and bi-univalent functions, we obtain estimates on coefficients and the Fekete-Szegö functional.
Citation: Luminiţa-Ioana Cotîrlǎ. New classes of analytic and bi-univalent functions[J]. AIMS Mathematics, 2021, 6(10): 10642-10651. doi: 10.3934/math.2021618
Using the (p, q)-derivative operator we introduce new subclasses of analytic and bi-univalent functions, we obtain estimates on coefficients and the Fekete-Szegö functional.
[1] | Ş. Altinkaya, S. Yalçin, Faber polynomial coefficient bounds for a subclass of bi-univalent functions. C. R. Math. Acad. Sci. Paris, 353 (2015), 1075–1080. |
[2] | R. Bucur, L. Andrei, D. Breaz, Coefficient bounds and Fekete-Szegö problem for a class of analytic functions defined by using a new differential operator. Appl. Math. Sci., 9 (2015), 1355–1368. |
[3] | A. Catas, Some inclusion relations for a certain family of multivalent functions involving nonhomogeneous Cauchy-Euler differential equation, An. Univ. Oradea Fasc. Mat., Tom XVII (2010), 51–64. |
[4] | R. B. Corcino, On $p, q$-binomial coefficients, Integers, 8 (2008), A29. |
[5] | P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften; Springer-Verlag, New York, 1983. |
[6] | J. Dziok, A general solution of the Fekete-Szegö problem, Bound. Value Probl., 2013 (2013), 1–13. doi: 10.1186/1687-2770-2013-1 |
[7] | S. M. El-Deeb, T. Bulboacǎ, B. M. El-Matary, Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative, Mathematics, 8 (2020), 418. doi: 10.3390/math8030418 |
[8] | M. Fekete, G. Szegö, Eine bemerkung über ungerade schlichte funktionen, J. Lond. Math. Soc., 8 (1933), 85–89. |
[9] | M. Govindaraj, S. Sivasubramanian, On a class of analytic functions related to conic domains involving q-calculus, Anal. Math., 43 (2017), 475–487. doi: 10.1007/s10476-017-0206-5 |
[10] | J. M. Jahangiri, S. G. Hamidi, Faber polynomial coefficient estimates for analytic bi-Bazilevic functions, Mat. Vesnik, 67 (2015), 123–129. |
[11] | S. Kanas, An unified approach to the Fekete-Szegö problem, Appl. Math. Comput., 218 (2012), 8453–8461. |
[12] | M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), 63–68. doi: 10.1090/S0002-9939-1967-0206255-1 |
[13] | W. Ma, D. Minda, A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis, 1992. |
[14] | A. O. Pall-Szabo, G. I. Oros, Coefficient Related Studies for New Classes of Bi-Univalent Functions, Mathematics, 8 (2020), 1110. doi: 10.3390/math8101793 |
[15] | C. Pommerenke, Univalent functions, Vanderhoeck and Ruprecht: Gottingen, Germany, 1975. |
[16] | P. N. Sadjang, On the fundamental theorem of (p, q)-calculus and some (p, q)-Taylor formulas, archiv: 1309.3934[math.QA]. |
[17] | S. Sivasubramanian, R. Sivakumar, S. Kanas, S-A. Kim, Verification of Brannan and Clunie's conjecture for certain sub- classes of bi-univalent functions, Ann. Polon. Math., 113 (2015), 295–304. doi: 10.4064/ap113-3-6 |
[18] | H. M. Srivastava, Ş. Altinkaya, S. Yalçin, Hankel Determinant for a Subclass of Bi-Univalent Functions Defined by Using a Symmetric q-Derivative Operator, Filomat, 32 (2018), 503–516. doi: 10.2298/FIL1802503S |
[19] | H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), 1188–1192. doi: 10.1016/j.aml.2010.05.009 |
[20] | A. K. Wanas, A. Alb Lupas, Applications of Horadam Polynomials on Bazilevic Bi- Univalent Function Satisfying Subordinate Conditions, Journal of Physics: Conf. Series, 1294 (2019), 032003. doi: 10.1088/1742-6596/1294/3/032003 |