Coefficient bounds for some subclasses of p-valently starlike functions

C. Selvaraj; O. S. Babu; G. Murugusundaramoorthy

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2013)

  • Volume: 67, Issue: 2
  • ISSN: 0365-1029

Abstract

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For functions of the form f ( z ) = z p + ∑ n = 1 ∞ a p + n z p + n we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szego-like inequality for classes of functions defined through extended fractional differintegrals are obtained.

How to cite

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C. Selvaraj, O. S. Babu, and G. Murugusundaramoorthy. "Coefficient bounds for some subclasses of p-valently starlike functions." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 67.2 (2013): null. <http://eudml.org/doc/289727>.

@article{C2013,
abstract = {For functions of the form \[f(z) = z^\{p\} + \sum \_\{n = 1\}^\{\infty \} a\_\{p + n\} z^\{p + n\}\] we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szego-like inequality for classes of functions defined through extended fractional differintegrals are obtained.},
author = {C. Selvaraj, O. S. Babu, G. Murugusundaramoorthy},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Analytic functions; starlike functions; convex functions; p-valent functions; subordination; convolution; Fekete-Szego inequality.},
language = {eng},
number = {2},
pages = {null},
title = {Coefficient bounds for some subclasses of p-valently starlike functions},
url = {http://eudml.org/doc/289727},
volume = {67},
year = {2013},
}

TY - JOUR
AU - C. Selvaraj
AU - O. S. Babu
AU - G. Murugusundaramoorthy
TI - Coefficient bounds for some subclasses of p-valently starlike functions
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2013
VL - 67
IS - 2
SP - null
AB - For functions of the form \[f(z) = z^{p} + \sum _{n = 1}^{\infty } a_{p + n} z^{p + n}\] we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szego-like inequality for classes of functions defined through extended fractional differintegrals are obtained.
LA - eng
KW - Analytic functions; starlike functions; convex functions; p-valent functions; subordination; convolution; Fekete-Szego inequality.
UR - http://eudml.org/doc/289727
ER -

References

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  1. Ali, R. M., Ravichandran, V., Seenivasagan, N., Coefficient bounds for p-valent functions, Appl. Math. Comput. 187 (2007), 35–46. 
  2. Janowski, W., Some extremal problems for certain families of analytic functions, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 21 (1973), 17–25. 
  3. Keogh, F. R., Merkes, E. P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8–12. 
  4. Ma, W. C., Minda, D., A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Int. Press, Cambridge, MA, 1994, 157–169. 
  5. Owa, S., On the distortion theorem. I, Kyungpook Math. J. 18 (1) (1978), 53–59. 
  6. Owa, S., Srivastava, H. M., Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (5) (1987), 1057–1077. 
  7. Patel, J., Mishra, A., On certain subclasses of multivalent functions associated with an extended differintegral operator, J. Math. Anal. Appl. 332 (2007), 109–122. 
  8. Prokhorov, D. V., Szynal, J., Inverse coefficients for ( α , β ) -convex functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 35 (1981), 125–143. 
  9. Selvaraj, C., Selvakumaran, K. A., Fekete–Szego problem for some subclass of analytic functions, Far East J. Math. Sci. (FJMS) 29 (3) (2008), 643–652. 
  10. Srivastava, H. M., Mishra, A. K., Das, M. K., The Fekete–Szego problem for a subclass of close-to-convex functions, Complex Variables Theory Appl. 44 (2) (2001), 145–163. 
  11. Srivastava, H. M., Owa, S., An application of the fractional derivative, Math. Japon. 29 (3) (1984), 383–389. 
  12. Srivastava, H. M., Owa, S., Univalent Functions, Fractional Calculus and their Applications, Halsted Press/John Wiley & Sons, Chichester–New York, 1989. 

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