In this paper, we obtain the Fekete-Szego inequalities for the functions of complex order defined by convolution. Also, we find upper bounds for the second Hankel determinant for functions belonging to the class .
@article{bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_47-59,
author = {S. M. El-Deeb and M. K. Aouf},
title = {Hankel determinant for a class of analytic functions of complex order defined by convolution},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {69},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_47-59}
}
S. M. El-Deeb; M. K. Aouf. Hankel determinant for a class of analytic functions of complex order defined by convolution. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 69 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_47-59/
Abubaker, A., Darus, M., Hankel determinant for a class of analytic functions involving a generalized linear differential operator, Internat. J. Pure Appl. Math. 69 (3) (2011), 429-435.
Al-Oboudi, F. M., On univalent functions defined by a generalized Salagean operator, Internat. J. Math. Math. Sci. 27 (2004), 1429-1436.
Aouf, M. K., Subordination properties for a certain class of analytic functions defined by the Salagean operator, Appl. Math. Lett. 22 (2009), 1581-1585.
Bansal, D., Upper bound of second Hankel determinant for a new class of analytic functions}, Appl. Math. Lett. 26 (1) (2013), 103-107.
Bansal, D., Fekete-Szego problem and upper bound of second Hankel determinant for a new class of analytic functions, Kyungpook Math. J. 54 (2014), 443-452.
Bulboaca, T., Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.
Catas, A., On certain classes of p-valent functions defined by multiplier transformations, in Proceedings of the International Symposium on Geometric Function Theory and Applications, (Istanbul, Turkey, August 2007), Istanbul, 2008, 241-250.
Cho, N. E., Srivastava, H. M., Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling 37 (1-2) (2003), 39-49.
Cho, N. E., Kim, T. H., Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40 (3) (2003), 399-410.
Duren, P. L., Univalent Functions, Springer-Verlag, New York, 1983.
Dziok, J., Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1-13.
Dziok, J., Srivastava, H. M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003), 7-18.
El-Ashwah, R. M., Aouf, M. K., Differential subordination and superordination for certain subclasses of p-valent functions, Math. Comput. Modelling 51 (2010), 349-360.
El-Ashwah, R. M., Aouf, M. K., Some properties of new integral operator, Acta Univ. Apulensis 24 (2010), 51-61.
Grenander, U., Szego, G., Toeplitz Forms and Their Application, Univ. of California Press, Berkeley, 1958.
Janteng, A., Halim, S. A., Darus, M., Hankel determinant for starlike and convex functions, Int. J. Math. Anal. (Ruse) 1 (13) (2007), 619-625.
Keogh, F. R., Markes, E. P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8-12.
Libera, R. J., Złotkewicz, E. J., Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc. 87 (2) (1983), 251-257.
Miller, S. S., Mocanu, P. T., Differential Subordination: Theory and Applications, Marcel Dekker Inc., New York-Basel, 2000.
Mishra, A. K., Gochhayat, P., Second Hankel determinant for a class of analytic functions defined by fractional derivative, Int. J. Math. Math. Sci. (2008), Art. ID 153280, 1-10.
Mishra, A. K., Kund, S. N., Second Hankel determinant for a class of functions defined by the Carlson-Shaffer, Tamkang J. Math. 44 (1) (2013), 73-82.
Mohammed, A., Darus, M., Second Hankel determinant for a class of analytic functions defined by a linear operator, Tamkang J. Math. 43 (3) (2012), 455-462.
Noonan, J. W., Thomas, D. K., On the second Hankel determinant of areally mean p-valent functions, Trans. Amer. Math. Soc. 223 (2) (1976), 337-346.
Prajapat, J. K., Subordination and superordination preserving properties for generalized multiplier transformation operator, Math. Comput. Modelling 55 (2012), 1456-1465.
Raina, R. K., Bansal, D., Some properties of a new class of analytic functions defined in tems of a Hadmard product, J. Inequal. Pure Appl. Math. 9 (2008), Art. 22, 1-9.
Rogosinski, W., On the coefficients of subordinate functions, Proc. London Math. Soc. 48 (1943), 48-82.
Salagean, G. S., Subclasses of univalent functions, in Complex analysis - fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), Springer-Verlag, Berlin, 1983, 362-372.
Selvaraj, C., Karthikeyan, K. R., Differential subordinant and superordinations for certain subclasses of analytic functions, Far East J. Math. Sci. 29 (2) (2008), 419-430.
Srivastava, H. M., Karlsson, P. W., Multiple Gaussian Hypergeometric Series, Ellis Horwood Limited, Chichester; Halsted Press, New York, 1985.