In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Some of our results improve and generalize previously known results.
@article{bwmeta1.element.doi-10_2478_v10062-010-0009-7,
author = {Mohamed Aouf and Tamer Seoudy},
title = {On differential sandwich theorems of analytic functions defined by certain linear operator},
journal = {Annales UMCS, Mathematica},
volume = {64},
year = {2010},
pages = {1-14},
zbl = {1213.30012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-010-0009-7}
}
Mohamed Aouf; Tamer Seoudy. On differential sandwich theorems of analytic functions defined by certain linear operator. Annales UMCS, Mathematica, Tome 64 (2010) pp. 1-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-010-0009-7/
Ali, R. M., Ravichandran, V. and Subramanian, K. G., Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci., 15(1) (2004), 87-94. | Zbl 1074.30022
Al-Oboudi, F., On univalent functions defined by a generalized Sălăgean operator, Internat. J. Math. Math. Sci. 27 (2004), 1429-1436. | Zbl 1072.30009
Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446.[Crossref] | Zbl 0172.09703
Bulboacă, T., Classes of first order differential superordinations, Demonstratio Math. 35(2) (2002), 287-292. | Zbl 1010.30020
Bulboacă, T., Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.
Carlson, B. C., Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745.[Crossref] | Zbl 0567.30009
Cătaş, A., Oros, G. I. and Oros, G., Differential subordinations associated with multiplier transformations, Abstr. Appl. Anal. 2008 (2008), Art. ID 845724, 1-11.[WoS] | Zbl 1153.30021
Cho, N. E., Kim, T. G., Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40(3) (2003), 399-410. | Zbl 1032.30007
Dziok, J., Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1-13.[Crossref][WoS] | Zbl 0937.30010
Dziok, J., Srivastava, H. M., Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function, Adv. Stud. Contemp. Math. (Kyungshang) 5 (2002), 115-125. | Zbl 1038.30009
Dziok, J., Srivastava, H. M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct. 14 (2003), 7-18.[Crossref] | Zbl 1040.30003
Hohlov, Yu. E., Operators and operations on the class of univalent functions, Izv. Vyssh. Uchebn. Zaved. Mat. 10 (1978), 83-89 (Russian).
Libera, R. J., Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965), 755-658.[Crossref] | Zbl 0158.07702
Livingston, A. E., On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 17 (1966), 352-357.[Crossref] | Zbl 0158.07701
Miller, S. S., Mocanu, P. T., Differential Subordination: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York, Basel, 2000.
Miller, S. S., Mocanu, P. T., Subordinates of differential superordinations, Complex Var. Theory Appl. 48(10) (2003), 815-826. | Zbl 1039.30011
Nechita, V. O., Differential subordinations and superordinations for analytic functions defined by the generalized Sălăgean derivative, Acta Univ. Apulensis 16 (2008), 143-156. | Zbl 1212.30054
Owa, S., Srivastava, H. M., Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), 1057-1077. | Zbl 0611.33007
Ruscheweyh, St., New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.[Crossref] | Zbl 0303.30006
Saitoh, H., A linear operator and its applications of first order differential subordinations, Math. Japon. 44 (1996), 31-38. | Zbl 0887.30021
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-Verlag, Berlin, 1983.
Selvaraj, C., Karthikeyan, K. R., Differential subordination and superordination for certain subclasses of analytic functions, Far East J. Math. Sci. (FJMS) 29(2) (2008), 419-430. | Zbl 1155.30335
Shanmugam, T. N., Ravichandran, V. and Sivasubramanian, S., Differential sandwich theorems for some subclasses of analytic functions, Aust. J. Math. Anal. Appl. 3(1) (2006), Art. 8, 1-11. | Zbl 1091.30019
Tuneski, N., On certain sufficient conditions for starlikeness, Internat. J. Math. Math. Sci. 23(8) (2000), 521-527.[Crossref] | Zbl 0954.30003