Coefficient inequality for subclass of analytic univalent functions related to simple logistic activation functions

Authors

  • Abiodun Tinuoye OLADIPO Department of Pure and Applied Mathematics Ladoke Akintola University of Technology, Ogbomoso P.M.B. 4000, Ogbomoso, Oyo State, Nigeria e-mail: atlab_3@yahoo.com https://orcid.org/0000-0001-6472-2430

Keywords:

Analytic, univalent, sigmoid, logistic activation, Fekete-Szegő, Sălăgean operator, coefficient inequalities.

Abstract

The author investigates the relationship between unified subclasses of analytic univalent functions and simple logistic activation function to determine the initial Taylor series coefficients alongside classical Fekete-Szegő problem.

Mathematics Subject Classification (2010): 30C45, 33E99.

References

El-Ashwah, R.M., Aouf, M.K., Hassan, A.H., Fekete-Szegő problem for a new class of analytic functions with complex order defined by certain differential operator, Stud. Univ. Babeș-Bolyai Math., 9(2014), no. 1, 25-36.

Fadipe-Joseph, O.A., Oladipo, A.T., Ezeafulukwe, U.A., Modified sigmoid function in univalent function theory, Internat. J. Math. Sci. Engr. Appl., 7(2013), no. 7, 313-317.

Fekete, M., Szegő, G., Eine bemerkung uber ungerade schlichte funktionen, J. Lond. Math. Soc., 8(1933), 85-89.

Janowski, W., Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math., 23(1970/1971), 159-177.

Keogh, F.R., Merkes, E.P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20(1969), 8-12.

Ma, W.C., Minda, D.A., A unified treatment of some special classes of univalent functions, in Proceedings of the Conference on Complex Analysis (Tianjin), 157-169, Conf. Proc. Lecture Notes Anal., I Int. press Cambridge, MA.

Miller, S.S., Mocanu, P.T., Differential subordinations, Monographs and Text Books in Pure and Applied Mathematics, 225, Dekker, New York, 2000.

Murugusundaramoorthy, G., Kavitha, S., Rosy, T., On the Fekete-Szegő problem for some subclasses of analytic functions defined by convolution, Proc. Pakistan Acad. Sci., 44(2), no. 4, 249-254.

Oladipo, A.T., Fadipe-Joseph, O.A., Iterated integral transforms of activated sigmoid function as related to Caratheodory family, Far East J. Appl. Math. (to appear).

Olatunji, S.O., Gbolagade, A.M., Anake, T., Fadipe-Joseph, O.A., Sigmoid function in the space of Univalent function of Bazilevic type, Sci. Magna J., 9(2013), no. 3, 43-51.

Ravichandran, V., Gangadharam, A., Darus, M., Fekete-Szegő inequality for certain class of Bazilevic functions, Far East J. Math. Sci., 15(2004), no. 2, 171-180.

Ravichandran, V., Darus, M., Khan, M.H., Subramanian, K.G., Fekete-Szegő inequality for certain class of analytic functions, Aust. J. Math. Anal. Appl., 1(2004), no. 2, Art. 4, 7 pp.

Sălăgean, G.S., Subclasses of univalent functions, Lecture Notes in Math., Springer-Verlag, 1013(1983), 362-372.

Kumar, S.S., Kumar, V., Fekete Szegő problem for a class of analytic functions, Stud. Univ. Babeș-Bolyai Math., 58(2013), no. 2, 181-188.

Srivastava, H.M., Mishra, A.K., Das, M.K., The Fekete-Szegő problem for a subclass of close-to-convex functions, Complex Variables Theory Appl., 44(2001), no. 2, 145-163.

Downloads

Published

2016-03-30

How to Cite

OLADIPO, A. T. (2016). Coefficient inequality for subclass of analytic univalent functions related to simple logistic activation functions. Studia Universitatis Babeș-Bolyai Mathematica, 61(1), 45–52. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/subbmathematica/article/view/5509

Issue

Section

Articles

Similar Articles

<< < 20 21 22 23 24 25 26 > >> 

You may also start an advanced similarity search for this article.