Bounds on third Hankel determinant for certain classes of analytic functions
Keywords:
Analytic, starlike and convex functions, Fekete-Szego¨ functional, Hankel determinants.Abstract
Mathematics Subject Classification (2010): 30C45, 30C50.References
Abdet Gawad, H.R., Thomas, D.K., The Fekete-Szeg¨o problem for strongly close-to- convex functions, Proc. Amer. Math. Soc., 114(1992), 345-349.
Al-Abbadi, M.H., Darus, M., Hankel determinant for certain class of analytic function defined by generalized derivative operators, Tamkang J. Math., 43(2012), 445-453.
Babalola, K.O., On third order Hankel determinant for some classes of univalent functions, Inequal. Theory Appl., 6(2010), 1-7.
Bansal, D., Upper bound of second Hankel determinant for a new class of analytic functions, Appl. Math. Lett., 26(2013), 103-107.
Bansal, D., Maharana, S., Prajapat, J.K., Third order Hankel determinant for certain univalent functions, J. Korean Math. Soc., 52(2015), no. 6, 1139-1148.
Cantor, D.G., Power series with the integral coefficients, Bull. Amer. Math. Soc., 69(1963), 362-366.
Duren, P.L., Univalent Functions, Springer Verlag, New Yark Inc. 1983.
Ehrenborg, R., The Hankel determinant of exponential polynomials, Amer. Math. Monthly, 107(2000), 557-560.
Fekete, M., Szego¨, G., Eine Benberkung uber ungerada Schlichte funktionen, J. Lond. Math. Soc., 8(1933), 85-89.
Hayman, W.K., On second Hankel determinant of mean univalent functions, Proc. Lond. Math. Soc., 18(1968), 77-94.
Jovanovic, I., Obradovi`c, M., A note on certain classes of univalent functions, Filomat, 9(1995), 69-72.
Keogh, F.R., Merkes, E.P., A Coefficient Inequality for Certain Classes of Analytic Functions, Proc. Amer. Math. Soc., 20(1969), 8-12.
Koepf, W., On the Fekete-Szeg¨o problem for close-to-convex functions, Proc. Amer. Math. Soc., 101(1987), 85-95.
Lee, S.K., Ravichandran, V., Supramaniam, S., Bounds for the second Hankel determinant of certain univalent functions, J. Inequal. Appl., 2013(2013), art. 281.
Li, J.L., Srivastava, H.M., Some questions and conjectures in the theory of univalent functions, Rocky Mountain J. Math., 28(1998), 1035-1041.
Libera, R.J., Zlotkiewicz, E.J., Early coefficients of the inverse of a regular convex function, Proc. Amer. Math. Soc., 85(1982), 225-230.
London, R.R., Fekete-Szeg¨o inequalities for close-to-convex functions, Proc. Amer. Math. Soc., 117(1993), 947-950.
Miller, S.S., Mocanu, P.T., Differential Subordinations. Theory and Applications, New York and Basel, Marcel Dekker, 2000.
Nishiwaki, J., Owa, S., Coefficient inequalities for certain analytic functions, Int. J. Math. Math. Sci., 29(2002), 285-290.
Noonan, J.W., Thomas, D.K., On the second Hankel determinant of areally mean p- valent functions, Trans. Amer. Math. Soc., 223(1976), 337-346.
Obradovi´c, M., Ponnusamy, S., Injectivity and starlikeness of section of a class of univalent functions, Contemporary Math., 591(2013), 195-203.
Obradovi´c, M., Ponnusamy, S., Wirths, K.-J., Coefficient characterizations and sections for some univalent functions, Sib. Math. J., 54(2013), 679-696.
Owa, S., Srivastava, H.M., Some generalized convolution properties associated with certain subclasses of analytic functions, J. Inequal. Pure Appl. Math., 3(2002), no. 3, art. 42, 13 pages.
Ozaki, S., On the theory of multivalent functions II, Sci. Rep. Tokyo Bunrika Daigaku. Sect A, 4(1941), 45-87.
Pommerenke, C., On the coefficients and Hankel determinant of univalent functions, J. Lond. Math. Soc., 41(1966), 111-122.
Pommerenke, C., On the Hankel determinant of univalent functions, Mathematika, 14(1967), 108-112.
Parvatham, R., Ponnusamy, S., (eds.) New trends in geometric function theory and application, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1981.
Prajapat, J.K., Bansal, D., Singh, A., Mishra, A.K., Bounds on third Hankel determinant for close-to-convex functions, Acta Univ. Sapientiae Math., 7(2015), no. 2, 210-219.
Raza, M., Malik, S.N., Upper bound of the third Hankel determinant for a class of analytic functions related with Lemniscate of Bernoulli, J. Inequal. Appl., 2013(2013), art. 412.
Shanmugam, T.N., Ramachandran, C., Ravichandran, V., Fekete-Szeg¨o problem for subclass of starlike functions with respect to symmetric points, Bull. Korean Math. Soc., 43(2006), no. 3, 589-598.
Srivastava, H.M., Mishra, A.K., Das, M.K., Fekete-Szeg¨o problem for a subclass of close- to-convex functions, Complex Var. Theory Appl., 44(2001), 145-163.
Uralegaddi, B.A., Ganigi, M.D., Sarangi, S.M., Univalent functions with positive coefficients, Tamkang J. Math., 25(1994), 225-230.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
