Journal of Mathematical Sciences and Applications
ISSN (Print): 2333-8784 ISSN (Online): 2333-8792 Website: http://www.sciepub.com/journal/jmsa Editor-in-chief: Prof. (Dr.) Vishwa Nath Maurya, Cenap ozel
Open Access
Journal Browser
Go
Journal of Mathematical Sciences and Applications. 2014, 2(1), 1-3
DOI: 10.12691/jmsa-2-1-1
Open AccessArticle

On the Second Hankel Determinant for a New Subclass of Analytic Functions

Gagandeep Singh1, and Gurcharanjit Singh2

1Department of Mathematics, M.S.K. Girls College, Bharowal (Tarn-Taran), Punjab, India

2Department of Mathematics, Guru Nanak Dev University College, Chungh (Tarn-Taran), Punjab, India

Pub. Date: February 10, 2014

Cite this paper:
Gagandeep Singh and Gurcharanjit Singh. On the Second Hankel Determinant for a New Subclass of Analytic Functions. Journal of Mathematical Sciences and Applications. 2014; 2(1):1-3. doi: 10.12691/jmsa-2-1-1

Abstract

In the present investigation an upper bound of the second Hankel determinant for the functions belonging to the class R(α;A,B) is studied. The results due to various authors follow as special cases.

Keywords:
analytic functions Subordination Schwarz function second Hankel determinant

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  R. M. Goel and B. S. Mehrok, A subclass of univalent functions, J. Austral. Math. Soc.(Series A), 35 (1983), 1-17.
 
[2]  Aini Janteng, Suzeini Abdul Halim and Maslina Darus, Coefficient inequality for a function whose derivative has a positive real part, J. Ineq. Pure Appl. Math., 7 (2) (2006), 1-5, Art. 50.
 
[3]  Aini Janteng, Suzeini Abdul Halim and Maslina Darus, Hankel determinant for starlike and convex functions, Int. J. Math. Anal., 1 (13) (2007), 619-625.
 
[4]  Aini Janteng, Suzeini Abdul Halim and Maslina Darus, Hankel determinant for functions starlike and convex with respect to symmetric points, J. Quality Measurement and Anal., 2 (1) (2006), 37-43.
 
[5]  R. J. Libera and E-J. Zlotkiewiez, Early coefficients of the inverse of a regular convex function, Proc. Amer. Math. Soc., 85 (1982), 225-230.
 
[6]  R. J. Libera and E-J. Zlotkiewiez, Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc., 87 (1983), 251-257.
 
[7]  T. H. Mac Gregor, Functions whose derivative has a positive real part, Trans. Amer. Math. Soc., 104 (1962), 532-537.
 
[8]  B. S. Mehrok and Gagandeep Singh, Estimate of second Hankel determinant for certain classes of analytic functions, Scientia Magna, 8 (3) (2012), 85-94.
 
[9]  G. Murugusundramurthi and N. Magesh, Coefficient inequalities for certain classes of analytic functions associated with Hankel determinant, Bull. Math. Anal. and Appl., 1 (3) (2009), 85-89.
 
[10]  J. W. Noonan and D. K. Thomas, On the second Hankel determinant of a really mean p-valent functions, Trans. Amer. Math. Soc., 223 (2) (1976), 337-346.
 
[11]  Ch. Pommerenke, Univalent functions, Göttingen: Vandenhoeck and Ruprecht, 1975.
 
[12]  Gagandeep Singh, Hankel determinant for new subclasses of analytic functions with respect to symmetric points, Int. J. of Modern Math. Sci., 5 (2) (2013), 67-76.
 
[13]  Gagandeep Singh, Hankel determinant for a new subclass of analytic functions, Scientia Magna, 8 (4) (2012), 61-65.