δ −POLYNOMIAL BOUNDS FOR A SUBCLASS OF UNIVALENT FUNCTION REGARDING MODIFIED SIGMOID FUNCTION
Keywords:
Salagean operator, Chebyshev polynomials, sigmoid function, Analytic functionAbstract
In this article, the authors investigated a new subclass of analytic univalent function which relate to ameliorated sigmoid function and the classical special polynomial function known as the Chebyshev polynomials by employing the concept of subordination. This investigation produced new interesting coefficient bounds. The famous Fekete-Szego inequalities were also pointed out.
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Fadipe - Joseph , O.A., Kadir, B.B., Akinwumi, S. E., and Adeniran, E.O., Polynomial Bounds for a class of univalent function involving sigmoid function, Khayyam J. Math., 4 (2018), no. 1 88 -101.
Oladipo, A.T., Coefficient inequality for subclass of analytic univalent functions related to simple logistic activation functions, Stud. Univ.Bolyai Math: 61 (2016), No. 1, 45 52.
Salagean, G.S., Subclasses of univalent functions, lecture notes in Mathematics, Springers Verlag, Berlin, 1013 (1983), 32 -372.
Pomerenke C.H., Univalent function with chapter on Quadratic Differentials, Gerd Jensen Vandenhoeck and Ruprecht in Gottingen, Germany, (1973).
Fadipe - Joseph, O.A., Oladipo, A.T., and Ezeafulukwe, A.U., Modified sigmoid function in univalent theory, Int. J. Math. Sci. Eng Appl., 7(v) (2013), 313 - 317.
Altinkaya, S., and Yalcin, S., On the Chebyshev polynomial bounds for classes of univalent functions, Khayyam J. Math., 2 (2016), no. 1. 1- 5.
Bulut, S., and Magesh, N., On the sharp bounds for a comprehensive class of analytic and univalent functions by means of Chebyshev polynomials, Khayyam J. Math., 2 (2016), no. 2, 194 - 200.
Whittaker, E.T., and Watson, G,N., A Course of Modern Analysis: An introduction to the general theory of infinite processes of analytic functions; with an account of the principal transcendental functions, 4 th ed., Cambridge University Press (1963).
Duren, P.L., Univalent functions, Springer Verlag, New York Inc., (1983).
Dziok, J., A general solution of the Fekete - Szego problem, boundary value problems, 98 (2013).
Fadipe - Joseph, O.A., Moses, B.O., and Oluwayemi, M.O., Certain new classes of analytic functions defined by using sigmoid function, Adv. Maths; Sci. J., 5 (2016), no. 1, 83 89.
Ramachandran, C., and Dhanalakshmi, K., Coefficient estimates for a class of spirallike function in the space of sigmoid function, Glob. J. Pure Appl. Math., 13 (2017), no.1, 13 - 19.
Ramachandran, C., and Dhanalakshmi, K., The Fekete - Szego problem for a subclass of analytic functions related to sigmoid function, Int., J. Pure Appl. Math., 113 (2017), no. 3, 389 - 398.
Ma, W., and Minda, D., a unified treatment of some classes of univalent functions, 1994, 157 -169.
Miller, S.S., and Mocanu, P. T., Differential subordination Monographs and Text books in Pure and Applied Mathematics, 225, Dekker, New York.
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