On subordination for classes of non-Bazilevič type

Rabha Ibrahim; Maslina Darus; Nikola Tuneski

Annales UMCS, Mathematica (2010)

  • Volume: 64, Issue: 2, page 49-60
  • ISSN: 2083-7402

Abstract

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We give some subordination results for new classes of normalized analytic functions containing differential operator of non-Bazilevič type in the open unit disk. By using Jack's lemma, sufficient conditions for this type of operator are also discussed.

How to cite

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Rabha Ibrahim, Maslina Darus, and Nikola Tuneski. "On subordination for classes of non-Bazilevič type." Annales UMCS, Mathematica 64.2 (2010): 49-60. <http://eudml.org/doc/268288>.

@article{RabhaIbrahim2010,
abstract = {We give some subordination results for new classes of normalized analytic functions containing differential operator of non-Bazilevič type in the open unit disk. By using Jack's lemma, sufficient conditions for this type of operator are also discussed.},
author = {Rabha Ibrahim, Maslina Darus, Nikola Tuneski},
journal = {Annales UMCS, Mathematica},
keywords = {Fractional calculus; subordination; non-Bazilevič; function; Jack's lemma; fractional calculus; non-Bazilevič function; Jack's Lemma},
language = {eng},
number = {2},
pages = {49-60},
title = {On subordination for classes of non-Bazilevič type},
url = {http://eudml.org/doc/268288},
volume = {64},
year = {2010},
}

TY - JOUR
AU - Rabha Ibrahim
AU - Maslina Darus
AU - Nikola Tuneski
TI - On subordination for classes of non-Bazilevič type
JO - Annales UMCS, Mathematica
PY - 2010
VL - 64
IS - 2
SP - 49
EP - 60
AB - We give some subordination results for new classes of normalized analytic functions containing differential operator of non-Bazilevič type in the open unit disk. By using Jack's lemma, sufficient conditions for this type of operator are also discussed.
LA - eng
KW - Fractional calculus; subordination; non-Bazilevič; function; Jack's lemma; fractional calculus; non-Bazilevič function; Jack's Lemma
UR - http://eudml.org/doc/268288
ER -

References

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  1. Darus, M., Ibrahim, R. W., Coefficient inequalities for a new class of univalent functions, Lobachevskii J. Math. 29(4) (2008), 221-229. Zbl1166.30302
  2. Ibrahim, R. W., Darus, M., On subordination theorems for new classes of normalize analytic functions, Appl. Math. Sci. (Ruse) 2(56) (2008), 2785-2794. Zbl1187.30018
  3. Ibrahim, R. W., Darus, M., Subordination for new classes of non-Bazilevič type, UNRI-UKM Symposium, KE-4 (2008). 
  4. Ibrahim, R. W., Darus, M., Differential subordination results for new classes of the family ε (Φ, Ψ), JIPAM. J. Ineq. Pure Appl. Math. 10(1) (2009), Art. 8, 9 pp. 
  5. Jack, I. S., Functions starlike and convex of order k, J. London Math. Soc. 3 (1971), 469-474.[Crossref] Zbl0224.30026
  6. Miller, S. S., Mocanu, P. T., Differential Subordinantions. Theory and Applications, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York, 2000. 
  7. Miller, K. S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, Inc., New York, 1993. Zbl0789.26002
  8. Obradovič, M., A class of univalent functions, Hokkaido Math. J. 27(2) (1998), 329-335. Zbl0908.30009
  9. Raina, R. K., On certain class of analytic functions and applications to fractional calculus operator, Integral Transform. Spec. Funct. 5 (1997), 247-260.[Crossref] Zbl0907.30013
  10. Raina, R. K., Srivastava, H. M., A certain subclass of analytic functions associated with operators of fractional calculus, Comput. Math. Appl. 32 (1996), 13-19.[Crossref] Zbl0867.30015
  11. Shanmugam, T. N., Ravichangran, V. and Sivasubramanian, S., Differential sandwich theorems for some subclasses of analytic functions, Austral. J. Math. Anal. Appl. 3(1) (2006), 1-11. 
  12. Srivastava, H. M., Owa, S. (Eds.), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press, John Wiley and Sons, New York, Chichester, Brisbane, Toronto, 1989. Zbl0683.00012
  13. Srivastava, H. M., Owa, S. (Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London, Hong Kong, 1992. Zbl0976.00007
  14. Tuneski, N., Darus, M., Fekete-Szegö functional for non-Bazilevič functions, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 18(2) (2002), 63-65. Zbl1017.30012
  15. Wang, Z., Gao, C. and Liao, M., On certain generalized class of non-Bazilevič functions, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 21(2) (2005), 147-154. Zbl1092.30032

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