Welcome to Open Science
Contact Us
Home Books Journals Submission Open Science Join Us News
Second Hankel Determinant for Subclasses of Starlike and Convex Functions
Current Issue
Volume 2, 2014
Issue 6 (December)
Pages: 48-51   |   Vol. 2, No. 6, December 2014   |   Follow on         
Paper in PDF Downloads: 70   Since Aug. 28, 2015 Views: 2147   Since Aug. 28, 2015
Authors
[1]
Gagandeep Singh, Department of Mathematics, M. S. K. Girls College, Bharowal (Tarn-Taran), Punjab, India.
[2]
Gurcharanjit Singh, Department of Mathematics, Guru Nanak Dev University College, Chungh (Tarn-Taran), Punjab, India.
Abstract
The present paper is concerned with the estimate of an upper bound of second Hankel determinant for the functions belonging to the subclasses of the classes of starlike and convex functions in the unit disc. Results proved by various authors can be obtained as special cases of the results of this paper by giving particular values to the parameters A and B.
Keywords
Analytic Functions, Starlike Functions, Convex Functions, Subordination, Schwarz Function, Second Hankel Determinant
Reference
[1]
R. M. Goel and B. S. Mehrok, On the coefficients of a subclass of starlike functions, Ind. J. Pure and Appl. Math., 12(5)(1981), 634-647.
[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 (2006), Hankel determinant for functions starlike and convex with respect to symmetric points, J. Quality Measurement and Anal., 2(1), 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]
B. S. Mehrok and Gagandeep Singh, Estimate of second Hankel determinant for certain classes of analytic functions, Scientia Magna, 8(3)(2012), 85-94.
[8]
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.
[9]
Ch. Pommerenke, Univalent functions, Göttingen: Vandenhoeck and Ruprecht., 1975.
[10]
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.
[11]
Gagandeep Singh, Hankel determinant for a new subclass of analytic functions, Scientia Magna, 8(4)(2012), 61-65.
[12]
Gagandeep Singh and Gurcharanjit Singh, On the second Hankel determinant for a new subclass of analytic functions, Journal of mathematical Sciences and Applications, 2(1)(2014), 1-3.
[13]
Gagandeep Singh and Gurcharanjit Singh, Hankel determinant for a subclass of alpha convex functions, Bonfring International Journal of Data Mining, 4(3)(2014), 16-21.
[14]
Gagandeep Singh and Gurcharanjit Singh, Second Hankel determinant for a subclass of alpha convex functions, Journal of Applied and Computational Mathematics, (2014), doi: 10.4172/2168-9679.1000167.
[15]
Gagandeep Singh and Gurcharanjit Singh, Upper bound of the Second Hankel determinant for a subclass of analytic functions, New Trends in Mathematical Sciences, 2(1)(2014), 53-58.
[16]
Gagandeep Singh and Gurcharanjit Singh, Estimate of Second Hankel determinant for a subclass of analytic functions with respect to symmetric points, Asia Pacific Journal of Mathematics, 1(2)(2014), 134-140.
[17]
Gagandeep Singh and Gurcharanjit Singh, Estimate of Second Hankel determinant for a subclass of p-valently alpha convex functions, Mathematical Sciences Research Journal, 17(5)(2013).
Open Science Scholarly Journals
Open Science is a peer-reviewed platform, the journals of which cover a wide range of academic disciplines and serve the world's research and scholarly communities. Upon acceptance, Open Science Journals will be immediately and permanently free for everyone to read and download.
CONTACT US
Office Address:
228 Park Ave., S#45956, New York, NY 10003
Phone: +(001)(347)535 0661
E-mail:
LET'S GET IN TOUCH
Name
E-mail
Subject
Message
SEND MASSAGE
Copyright © 2013-, Open Science Publishers - All Rights Reserved