Coefficient bounds for some subclasses of p-valently starlike functions

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

Annales UMCS, Mathematica (2013)

  • Volume: 67, Issue: 2, page 65-78
  • ISSN: 2083-7402

Abstract

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For functions of the form f(z) = zp + ∑∞n=1 ap+n zp+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-Szegö-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 UMCS, Mathematica 67.2 (2013): 65-78. <http://eudml.org/doc/267938>.

@article{C2013,
abstract = {For functions of the form f(z) = zp + ∑∞n=1 ap+n zp+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-Szegö-like inequality for classes of functions defined through extended fractional differintegrals are obtained},
author = {C. Selvaraj, O. S. Babu, G. Murugusundaramoorthy},
journal = {Annales UMCS, Mathematica},
keywords = {Analytic functions; starlike functions; convex functions; pvalent functions; subordination; convolution; Fekete-Szegö inequality; analytic functions; -valent functions},
language = {eng},
number = {2},
pages = {65-78},
title = {Coefficient bounds for some subclasses of p-valently starlike functions},
url = {http://eudml.org/doc/267938},
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 UMCS, Mathematica
PY - 2013
VL - 67
IS - 2
SP - 65
EP - 78
AB - For functions of the form f(z) = zp + ∑∞n=1 ap+n zp+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-Szegö-like inequality for classes of functions defined through extended fractional differintegrals are obtained
LA - eng
KW - Analytic functions; starlike functions; convex functions; pvalent functions; subordination; convolution; Fekete-Szegö inequality; analytic functions; -valent functions
UR - http://eudml.org/doc/267938
ER -

References

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  1. [1] Ali, R. M., Ravichandran, V., Seenivasagan, N., Coefficient bounds for p-valent functions, Appl. Math. Comput. 187 (2007), 35-46.[Crossref] Zbl1113.30024
  2. [2] Janowski, W., Some extremal problems for certain families of analytic functions, Bull. Acad. Polon. Sci. S´er. Sci. Math. Astronom. Phys. 21 (1973), 17-25. Zbl0252.30021
  3. [3] Keogh, F. R., Merkes, E. P., A coefficient inequality for certain classes of analyticfunctions, Proc. Amer. Math. Soc. 20 (1969), 8-12.[Crossref] Zbl0165.09102
  4. [4] Ma, W. C., Minda, D., A unified treatment of some special classes of univalentfunctions, Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Int. Press, Cambridge, MA, 1994, 157-169. Zbl0823.30007
  5. [5] Owa, S., On the distortion theorem. I, Kyungpook Math. J. 18 (1) (1978), 53-59. Zbl0401.30009
  6. [6] Owa, S., Srivastava, H. M., Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (5) (1987), 1057-1077. Zbl0611.33007
  7. [7] Patel, J., Mishra, A., On certain subclasses of multivalent functions associated withan extended differintegral operator, J. Math. Anal. Appl. 332 (2007), 109-122.[Crossref] Zbl1125.30010
  8. [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. [9] Selvaraj, C., Selvakumaran, K. A., Fekete-Szeg¨o problem for some subclass of analyticfunctions, Far East J. Math. Sci. (FJMS) 29 (3) (2008), 643-652. Zbl1160.30330
  10. [10] Srivastava, H. M., Mishra, A. K., Das, M. K., The Fekete-Szeg¨o problem for a subclassof close-to-convex functions, Complex Variables Theory Appl. 44 (2) (2001), 145-163. 
  11. [11] Srivastava, H. M., Owa, S., An application of the fractional derivative, Math. Japon. 29 (3) (1984), 383-389. Zbl0522.30011
  12. [12] Srivastava, H. M., Owa, S., Univalent Functions, Fractional Calculus and their Applications, Halsted Press/John Wiley & Sons, Chichester-New York, 1989. Zbl0683.00012

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