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On the Fekete–Szegö Problem for Certain Subclass of Analytic Functions

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 236)

Abstract

The purpose of the present investigation is to derive several Fekete–Szegö-type coefficient inequalities for certain subclasses of normalized analytic function \(f(z)\) defined in the open unit disk. Various applications of our main results involving (for example) the operators defined using generalized fractional differential operator are also considered. Thus, as one of these applications of our result, we obtain the Fekete–Szegö-type inequality for a class of normalized analytic functions, which is defined here by means of the convolution and the fractional differential operators.

Keywords

Starlike functions Fekete–Szegö problem Fractional derivatives Generalized Ruscheweyh derivative Convolution 

References

  1. 1.
    Bansal, D.: Fekete -Szegö problem for a new class of analytic function. Int. J. Math. Math. Sci., article ID 143096, 5 pp (2011)Google Scholar
  2. 2.
    Goyal, S.P., Goyal, R.: On a class of multivalent functions defined by generalized Ruscheweyh derivatives involving a general fractional derivative operator. J. Indian Acad. Math. 27(2), 439–456 (2005)Google Scholar
  3. 3.
    Koepf, W.: On the Fekete-Szegö problem for close-to-convex functions. Archiv derMathematik 49(5), 420–433 (1987)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Li, J.L.: On some classes of analytic functions. Mathematica Japonica 40(3), 523–529 (1994)MATHMathSciNetGoogle Scholar
  5. 5.
    Libera, R.J., Złotkiewicz, E.J.: Coefficient bounds for the inverse of a function with derivative in \(\rho \). Proc. Am. Math. Soc. 87(2), 251–257 (1983)MATHGoogle Scholar
  6. 6.
    London, R.R.: Fekete-Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc. 117(4), 947–950 (1993)MATHMathSciNetGoogle Scholar
  7. 7.
    Ma, W., Minda, D.: A unified treatment of some special classes of univalent functions. In: Li, Z., Ren, F., Yang, L., Zhang, S. (eds.) Proceedings of the Conference on Complex Analysis, pp. 157–169. Conference Proceedings and Lecture Notes in Analysis, vol. I. International Press, Cambridge, Massachusetts (1994)Google Scholar
  8. 8.
    Najafzadeh, S.: Application of Salagean and Ruscheweyh operators on univalent holomorphic functions with finitely many coefficients. Fractional Calculus Appl. Anal. 13(5), 517–520 (2010)MATHMathSciNetGoogle Scholar
  9. 9.
    Owa, S., Uralegaddi, B.A.: A class of functions \(\alpha \)- prestarlike of order \(\beta \). Bull. Korean Math. Soc. 21(4), 77–85 (1984)MATHMathSciNetGoogle Scholar
  10. 10.
    Owa, S., Srivastava, H.M.: Univalent and starlike generalized hypergeometric functions. Canad. J. Math. 39, 1057–1077 (1987)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Owa, S.: On the distortion theorems I. Kyungpook Math. J. 18, 53–58 (1978)MATHMathSciNetGoogle Scholar
  12. 12.
    Ponnusamy, S., Ronning, F.: Integral transforms of a class of analytic functions. Complex Variables Elliptic Equ. 53(5), 423–434 (2008)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Parihar, H.S., Agarwal, R.: Application of generalized Ruscheweyh derivatives on p-valent functions. J. Math. Appl. 34, 75–86 (2011)Google Scholar
  14. 14.
    Ponnusamy, S.: Neighborhoods and Carathėodory functions. J. Anal. 4, 41–51 (1996)MATHMathSciNetGoogle Scholar
  15. 15.
    Salagean, G.S.: Subclasses of univalent functions. Lect. Notes Math. 1983, 362–372 (1013)Google Scholar
  16. 16.
    Srivastava, H.M., Saxena, R.K.: Operators of fractional integration and their applications. Appl. Math. Comput. 118, 1–52 (2001)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Swaminathan, A.: Certain sufficiency conditions on Gaussian hypergeometric functions. J. Inequalities Pure Appl. Math. 5(4), article 83, 6 pp (2004)Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Malviya National Institute of TechnologyJaipurIndia
  2. 2.JECRC UDML College of EngineeringJaipurIndia

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