Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions

Orhan, Halit;Yagmur, Nihat;Caglar, Murat

  • 투고 : 2011.03.16
  • 심사 : 2012.07.24
  • 발행 : 2013.03.23


In this present work, the authors obtain Fekete-Szeg$\ddot{o}$ inequality for certain normalized analytic function $f(z)$ defined on the open unit disk for which $$\frac{{\lambda}{\beta}z^3(L(a,c)f(z))^{{\prime}{\prime}{\prime}}+(2{\lambda}{\beta}+{\lambda}-{\beta})z^2(L(a,c)f(z))^{{\prime}{\prime}}+z(L(a,c)f(z))^{{\prime}}}{{\lambda}{\beta}z^2(L(a,c)f(z))^{{\prime}{\prime}}+({\lambda}-{\beta})z(L(a,c)f(z))^{\prime}+(1-{\lambda}+{\beta})(L(a,c)f(z))}\;(0{\leq}{\beta}{\leq}{\lambda}{\leq}1)$$ lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamard product (or convolution) are given. As a special case of this result, Fekete-Szeg$\ddot{o}$ inequality for a class of functions defined through fractional derivatives are obtained.


Fekete-Szeg$\ddot{o}$ problem;Analytic function;Coefficient inequality


  1. F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1993), 189-196.
  2. 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), 145-163.
  3. B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., l5(1984), 737-745.
  4. E. Deniz and H. Orhan, The Fekete-Szego Problem for A Generalized Subclass of Analytic Functions, Kyungpook Math. J., 50(2010), 37-47.
  5. A. W. Goodman, Uniformly convex functions, Ann. Polon. Math., 56(1991), 87-92.
  6. W. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in Proceeding of the conference on complex analysis, Z. Li, F. Ren, L. Yang and S. Zhang (Eds.), Int. Press, (1994), 157-169.
  7. H. Orhan and E. Gunes, Fekete-Szego Inequality for Certain Subclass of Analytic Functions, General Math., 14(1)(2005), 41-54.
  8. H. Orhan and D. Raducanu, Fekete-Szego problem for strongly starlike functions associated with generalized hypergeometric functions, Math. Comput. Modelling, 50(2009), 430-438.
  9. H. Orhan, E. Deniz and D. Raducanu, The Fekete-Szego problem for subclasses of analytic functions defined by a differential operator related to conic domains, Comput. Math. Appl., 59(2010), 283-295.
  10. H. Orhan, N. Yagmur and E. Deniz, Coefficient Inequality For A Generalized Subclass Of Analytic Functions, Bulletin of the Trans. Univ. of Brasov, Vol 4(53), No. 1 - 2011 Series III: Mathematics, Informatics, Physics, 51-58.
  11. S. Owa and H. M. Srivastava, Univalent and starlike functions generalized by hypergeometric functions, Canad. J. Math., 39(1987), 1057-1077.

피인용 문헌

  1. Coefficient Bounds for Certain Analytic Functions 2016,