Research article

New classes of analytic and bi-univalent functions

  • Received: 28 May 2021 Accepted: 06 July 2021 Published: 23 July 2021
  • MSC : 30C45, 30C50

  • 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

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  • 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.



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    [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
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