Geodesic
On certain general integral operators of analytic functions
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 66 (2012) no. 1.

Voir la notice de l'article provenant de la source Library of Science

In this paper, we obtain new sufficient conditions for the operators F_α_1,α_2,...,α_n,β(z) and G_α_1,α_2,...,α_n,β(z) to be univalent in the open unit disc 𝒰, where the functions f_1, f_2,..., f_n belong to the classes S^*(a, b) and 𝒦(a, b). The order of convexity for the operators F_α_1,α_2,...,α_n,β(z) and G_α_1,α_2,...,α_n,β(z) is also determined. Furthermore, and for β= 1, we obtain sufficient conditions for the operators F_n(z) and G_n(z) to be in the class 𝒦(a, b). Several corollaries and consequences of the main results are also considered.
Keywords: Analytic functions, starlike and convex functions, integral operator 
@article{AUM_2012_66_1_a4,
     author = {Frasin, B. A.},
     title = {On certain general integral operators of analytic functions},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {66},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2012_66_1_a4/}
}
TY  - JOUR
AU  - Frasin, B. A.
TI  - On certain general integral operators of analytic functions
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2012
VL  - 66
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2012_66_1_a4/
LA  - en
ID  - AUM_2012_66_1_a4
ER  - 
%0 Journal Article
%A Frasin, B. A.
%T On certain general integral operators of analytic functions
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2012
%V 66
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2012_66_1_a4/
%G en
%F AUM_2012_66_1_a4
Frasin, B. A. On certain general integral operators of analytic functions. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 66 (2012) no. 1. http://geodesic.mathdoc.fr/item/AUM_2012_66_1_a4/

[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., Lownersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen, J. Reine Angew. Math. 255 (1972), 23-43.

[3] Becker, J., Lownersche Differentialgleichung und Schlichtheitskriterien, Math. Ann. 202 (1973), 321-335.

[4] Breaz, D., Univalence properties for a general integral operator, Bull. Korean Math. Soc. 46 (2009), no. 3, 439-446.

[5] Breaz, D., Breaz, N., Two integral operators, Studia Universitatis Babes-Bolyai Math., 47 (2002), no. 3, 13-19.

[6] Breaz, D., Breaz, N., Univalence conditions for certain integral operators, Studia Universitatis Babes-Bolyai, Mathematica, 47 (2002), no. 2, 9-15.

[7] Breaz, D., Owa, S., Some extensions of univalent conditions for certain integral operators, Math. Inequal. Appl., 10 (2007), no. 2, 321-325.

[8] Bulut, S., Univalence preserving integral operators defined by generalized Al- Oboudi differential operators, An. S¸tiint¸. Univ. ”Ovidius” Constant¸a Ser. Mat. 17 (2009), no. 1, 37-50.

[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, Birkhauser, Basel, 1983.

[10] Frasin, B. A., General integral operator defined by Hadamard product, Mat. Vesnik 62 (2010), no. 2, 127-136.

[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.

[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 Stoılow (Brasov, 1987), 43-48, Univ. Brasov, Brasov, 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.

[15] Seenivasagan, N., Sufficient conditions for univalence, Applied Math. E-Notes, 8 (2008), 30-35.

[16] Seenivasagan, N., Breaz, D., Certain sufficient conditions for univalence, Gen. Math. 15 (2007), no. 4, 7-15.