Browse > Article
http://dx.doi.org/10.4134/BKMS.2006.43.3.589

FEKETE-SZEGÖ PROBLEM FOR SUBCLASSES OF STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC POINTS  

Shanmugam, T.N. (Department of Mathematics, College of Engineering, Anna University)
Ramachandram, C. (Department of Mathematics, College of Engineering, Anna University)
Ravichandran, V. (School of Mathematical Sciences, Universiti Sains Malaysia)
Publication Information
Bulletin of the Korean Mathematical Society / v.43, no.3, 2006 , pp. 589-598 More about this Journal
Abstract
In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.
Keywords
analytic functions; starlike functions; convex functions; subordination; coefficient problem; $Fekete-Szeg\"{o}$ inequality;
Citations & Related Records

Times Cited By SCOPUS : 6
연도 인용수 순위
1 A. W. Goodman, Uniformly convex functions, Ann. Polon. Math. 56 (1991), no. 1, 87-92   DOI
2 W. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, Z. Li, F. Ren, L. Yang, and S. Zhang(Eds.), Internat. Press (1994), 157-169
3 S. Owa, On the distortion theorems I, Kyungpook Math. J. 18 (1978), no. 1, 53-59
4 S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), no. 5, 1057-1077   DOI
5 V. Ravichandran, A. Gangadharan, and M. Darus, Fekete-Szego inequality for certain class of Bazilevic functions, Far East J. Math. Sci. (FJMS) 15 (2004), no. 2, 171-180
6 F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993), no. 1, 189-196
7 K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72-75   DOI
8 H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 37 (1985), no. 1, 48-61   DOI
9 H. M. Srivastava, A. K. Mishra, and M. K. Das, The Fekete-Szego problem for a subclass of close-to-convex functions, Complex Variables Theory Appl. 44 (2001), no. 2, 145-163   DOI
10 H. M. Srivastava and S. Owa, An application of the fractional derivative, Math. Japon. 29 (1984), no. 3, 383-389
11 W. Janowski, Some extremal problems for certain families of analytic functions, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. 21 (1973), 17-25
12 B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), no. 4, 737-745   DOI
13 M. Darus and D. K. Thomas, On the Fekete-Szego theorem for close-to-convex functions, Math. Japon. 44 (1996), no. 3, 507-511
14 B. A. Frasin and M. Darus, On the Fekete-Szego problem, Int. J. Math. Math. Sci. 24 (2000), no. 9, 577-581   DOI   ScienceOn
15 H. M. Srivastava and S. Owa, Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press/John Wiley and Songs, Chichester/New York, 1989
16 M. Darus and D. K. Thomas, On the Fekete-Szego theorem for close-to-convex functions, Math. Japon. 47 (1998), no. 1, 125-132
17 N. Tuneski and M. Darus, Fekete-Szego functional for non-Bazilevic functions, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 18 (2002), no. 2, 63-65
18 V. Ravichandran, M. Darus, M. Hussain Khan, and K. G. Subramanian, Fekete-Szego inequality for certain class of analytic functions, Aust. J. Math. Anal. Appl. 1 (2004), no. 2, Art. 4, 7, pp
19 V. Ravichandran, Starlike and convex functions with respect to conjugate points, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 20 (2004), no. 1, 31-37