On certain general integral operators of analytic functions

B. Frasin

Annales UMCS, Mathematica (2012)

  • Volume: 66, Issue: 1, page 13-23
  • ISSN: 2083-7402

Abstract

top
In this paper, we obtain new sufficient conditions for the operators Fα1,α2,…,αn,β(z) and Gα1,α2,…,αn,β(z) to be univalent in the open unit disc U, where the functions f1, f2, …, fn belong to the classes S*(a, b) and K(a, b). The order of convexity for the operators Fα1,α2,…,αn,β(z) and Gα1,α2,…,αn,β(z) is also determined. Furthermore, and for β = 1, we obtain sufficient conditions for the operators Fn(z) and Gn(z) to be in the class K(a, b). Several corollaries and consequences of the main results are also considered.

How to cite

top

B. Frasin. "On certain general integral operators of analytic functions." Annales UMCS, Mathematica 66.1 (2012): 13-23. <http://eudml.org/doc/268168>.

@article{B2012,
abstract = {In this paper, we obtain new sufficient conditions for the operators Fα1,α2,…,αn,β(z) and Gα1,α2,…,αn,β(z) to be univalent in the open unit disc U, where the functions f1, f2, …, fn belong to the classes S*(a, b) and K(a, b). The order of convexity for the operators Fα1,α2,…,αn,β(z) and Gα1,α2,…,αn,β(z) is also determined. Furthermore, and for β = 1, we obtain sufficient conditions for the operators Fn(z) and Gn(z) to be in the class K(a, b). Several corollaries and consequences of the main results are also considered.},
author = {B. Frasin},
journal = {Annales UMCS, Mathematica},
keywords = {Analytic functions; starlike and convex functions; integral operator; starlike functions; convex functions},
language = {eng},
number = {1},
pages = {13-23},
title = {On certain general integral operators of analytic functions},
url = {http://eudml.org/doc/268168},
volume = {66},
year = {2012},
}

TY - JOUR
AU - B. Frasin
TI - On certain general integral operators of analytic functions
JO - Annales UMCS, Mathematica
PY - 2012
VL - 66
IS - 1
SP - 13
EP - 23
AB - In this paper, we obtain new sufficient conditions for the operators Fα1,α2,…,αn,β(z) and Gα1,α2,…,αn,β(z) to be univalent in the open unit disc U, where the functions f1, f2, …, fn belong to the classes S*(a, b) and K(a, b). The order of convexity for the operators Fα1,α2,…,αn,β(z) and Gα1,α2,…,αn,β(z) is also determined. Furthermore, and for β = 1, we obtain sufficient conditions for the operators Fn(z) and Gn(z) to be in the class K(a, b). Several corollaries and consequences of the main results are also considered.
LA - eng
KW - Analytic functions; starlike and convex functions; integral operator; starlike functions; convex functions
UR - http://eudml.org/doc/268168
ER -

References

top
  1. Ahlfors, L. V., Sufficient conditions for quasiconformal extension, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973), pp. 23-29. Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, N.J., 1974. 
  2. Becker, J., Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen, J. Reine Angew. Math. 255 (1972), 23-43. Zbl0239.30015
  3. Becker, J., Löwnersche Differentialgleichung und Schlichtheitskriterien, Math. Ann. 202 (1973), 321-335. Zbl0236.30024
  4. Breaz, D., Univalence properties for a general integral operator, Bull. Korean Math. Soc. 46 (2009), no. 3, 439-446.[Crossref][WoS] Zbl1163.30015
  5. Breaz, D., Breaz, N., Two integral operators, Studia Universitatis Babeş-Bolyai Math., 47 (2002), no. 3, 13-19. Zbl1027.30018
  6. Breaz, D., Breaz, N., Univalence conditions for certain integral operators, Studia Universitatis Babeş-Bolyai, Mathematica, 47 (2002), no. 2, 9-15. Zbl1027.30046
  7. Breaz, D., Owa, S., Some extensions of univalent conditions for certain integral operators, Math. Inequal. Appl., 10 (2007), no. 2, 321-325. Zbl1198.30011
  8. Bulut, S., Univalence preserving integral operators defined by generalized Al- Oboudi differential operators, An. Ştiinţ. Univ. "Ovidius" Constanţa Ser. Mat. 17 (2009), no. 1, 37-50. Zbl1249.30023
  9. 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. 
  10. Frasin, B. A., General integral operator defined by Hadamard product, Mat. Vesnik, 62 (2010), no. 2, 127-136. Zbl1265.30053
  11. Frasin. B. A., Aouf, M. K., Univalence conditions for a new general integral operator, Hacet. J. Math. Stat., 39 (2010), no. 4, 567-575. Zbl1237.47050
  12. Jabkubowski, Z. J., On the coefficients of starlike functions of some classes, Ann. Polon. Math. 26 (1972), 305-313. 
  13. Pascu, N., An improvement of Becker's univalence criterion, Proceedings of the Commemorative Session: Simion Stoïlow (Braşov, 1987), 43-48, Univ. Braşov, Braşov, 1987. 
  14. Pescar, V., A new generalization of Ahlfor's and Becker's criterion of univalence, Bull. Malaysian Math. Soc. (2) 19 (1996), no. 2, 53-54. Zbl0880.30020
  15. Seenivasagan, N., Sufficient conditions for univalence, Applied Math. E-Notes, 8 (2008), 30-35. Zbl1161.30316
  16. Seenivasagan, N., Breaz, D., Certain sufficient conditions for univalence, Gen. Math. 15 (2007), no. 4, 7-15. Zbl1199.30161

NotesEmbed ?

top

You must be logged in to post comments.