Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator

M. Aouf; A. Shamandy; A. Mostafa; S. Madian

Annales UMCS, Mathematica (2010)

  • Volume: 64, Issue: 1, page 17-26
  • ISSN: 2083-7402

Abstract

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Let A denote the class of analytic functions with the normalization f(0) = f'(0) - 1 = 0 in the open unit disc U = {z : |z| < 1}. Set [...] and define ∞nλ, μ in terms of the Hadamard product [...] . In this paper, we introduce several subclasses of analytic functions defined by means of the operator Inλ, μ A → A, given by [...] . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

How to cite

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M. Aouf, et al. "Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator." Annales UMCS, Mathematica 64.1 (2010): 17-26. <http://eudml.org/doc/268253>.

@article{M2010,
abstract = {Let A denote the class of analytic functions with the normalization f(0) = f'(0) - 1 = 0 in the open unit disc U = \{z : |z| < 1\}. Set [...] and define ∞nλ, μ in terms of the Hadamard product [...] . In this paper, we introduce several subclasses of analytic functions defined by means of the operator Inλ, μ A → A, given by [...] . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.},
author = {M. Aouf, A. Shamandy, A. Mostafa, S. Madian},
journal = {Annales UMCS, Mathematica},
keywords = {Analytic; Hadamard product; starlike; convex; analytic function; starlike function; convex function},
language = {eng},
number = {1},
pages = {17-26},
title = {Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator},
url = {http://eudml.org/doc/268253},
volume = {64},
year = {2010},
}

TY - JOUR
AU - M. Aouf
AU - A. Shamandy
AU - A. Mostafa
AU - S. Madian
TI - Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator
JO - Annales UMCS, Mathematica
PY - 2010
VL - 64
IS - 1
SP - 17
EP - 26
AB - Let A denote the class of analytic functions with the normalization f(0) = f'(0) - 1 = 0 in the open unit disc U = {z : |z| < 1}. Set [...] and define ∞nλ, μ in terms of the Hadamard product [...] . In this paper, we introduce several subclasses of analytic functions defined by means of the operator Inλ, μ A → A, given by [...] . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.
LA - eng
KW - Analytic; Hadamard product; starlike; convex; analytic function; starlike function; convex function
UR - http://eudml.org/doc/268253
ER -

References

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  1. Al-Oboudi, F. M., On univalent functions defined by a generalized Sălăgean operator, Internat. J. Math. Math. Sci. 27 (2004), 1429-1436. Zbl1072.30009
  2. Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc. 35 (1969), 429-446. Zbl0172.09703
  3. Choi, J. H., Saigo, M. and Srivastava, H. M., Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002), 432-445. Zbl1035.30004
  4. Eenigenburg, P., Miller, S. S., Mocanu, P. T. and Reade, M. O., On a Briot-Bouquet differential subordination, General inequalities, 3 (Oberwolfach, 1981), 339-348, Internat. Schriftenreihe Numer. Math., 64, Birkhäuser, Basel, 1983. 
  5. Kim, Y. C., Choi, J. H. and Sugawa, T., Coefficient bounds and convolution properties for certain classes of close-to-convex functions, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), 95-98. Zbl0965.30006
  6. Libera, R. J., Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965), 755-758. Zbl0158.07702
  7. Ma, W. C., Minda, D., An internal geometric characterization of strongly starlike functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 45 (1991), 89-97. 
  8. Miller, S. S., Mocanu, P. T., Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 157-171. Zbl0439.30015
  9. Owa, S., Srivastava, H. M., Some applications of the generalized Libera operator, Proc. Japan Acad. Ser. A Math. Sci. 62 (1986), 125-128. Zbl0583.30016
  10. Sălăgean, G. S., Subclasses of univalent functions, Complex analysis - fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math., 1013, Springer, Berlin, 1983. 
  11. Srivastava, H. M., Owa, S. (Editors), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, 1992. Zbl0976.00007

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