In the present paper, we apply methods based on differential subordinations and superordinations in order to derive several subordination results for multivalent functions involving the Hadamard product.
@article{bwmeta1.element.doi-10_2478_v10062-008-0001-7, author = {O. Ahuja and G. Murugusundaramoorthy and S. Sivasubramanian}, title = {Differential sandwich theorems for multivalent functions}, journal = {Annales UMCS, Mathematica}, volume = {62}, year = {2008}, pages = {1-13}, zbl = {1179.30018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-008-0001-7} }
O. Ahuja; G. Murugusundaramoorthy; S. Sivasubramanian. Differential sandwich theorems for multivalent functions. Annales UMCS, Mathematica, Tome 62 (2008) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-008-0001-7/
Ali, R. M., Ravichandran, V., Khan, M. Hussain and Subramanian, K. G., Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci. 15 (2004), no. 1, 87-94. | Zbl 1074.30022
Bulboacă, T., A class of superordination-preserving integral operators, Indag. Math. (N. S.) 13 (2002), no. 3, 301-311. | Zbl 1019.30023
Bulboacă, T., Classes of first-order differential superordinations, Demonstratio Math. 35 (2002), no. 2, 287-292. | Zbl 1010.30020
Carlson, B. C., Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745. | Zbl 0567.30009
Cho, N. E., Kim, T. H., Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40 (2003), no. 3, 399-410. | Zbl 1032.30007
Cho, N. E., Srivastava, H. M., Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling 37 (2003), no. 1-2, 39-49. | Zbl 1050.30007
Dziok, J., Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), no. 1, 1-13.[Crossref][WoS] | Zbl 0937.30010
Miller, S. S., Mocanu, P. T., Differential Subordinations. Theory and Applications, Marcel Dekker, New York, 2000. | Zbl 0954.34003
Miller, S. S., Mocanu, P. T., Subordinants of differential superordinations, Complex Var. Theory Appl. 48 (2003), no. 10, 815-826. | Zbl 1039.30011
Murugusundaramoorthy, G., Magesh, N., Differential subordinations and superordinations for analytic functions defined by the Dziok-Srivastava linear operator, J. Inequal. Pure Appl. Math. 7 (2006), no. 4, Art. 152, 9 pp. (electronic). | Zbl 1131.30315
Obradović, M., Owa, S., On certain properties for some classes of starlike functions, J. Math. Anal. Appl. 145 (1990), no. 2, 357-364.[Crossref] | Zbl 0707.30009
Patel, J., Cho, N. E., Some classes of analytic functions involving Noor integral operator, J. Math. Anal. Appl. 312 (2005), no. 2, 564-575.[Crossref] | Zbl 1082.30010
Ravichandran, V., Darus, M., Khan, Hussain M. and Subramanian, K. G., Differential subordination associated with certain linear operators defined by multivalent functions, Acta Math. Vietnam. 30 (2005), no. 2, 113-121. | Zbl 1155.30334
Ruscheweyh, S., New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.[Crossref] | Zbl 0303.30006
Sălăgean, G. Ş., Subclasses of univalent functions, Complex analysis - fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math., 1013, Springer, Berlin, 1983, 362-372.
Shanmugam, T. N., Convolution and differential subordination, Internat. J Math. Math. Sci. 12 (1989), no. 2, 333-340.[Crossref] | Zbl 0683.30023
Shanmugam, T. N., Ravichandran, V. and Sivasubramanian, S., Differential sandwich theorems for some subclasses of analytic functions, Aust. J. Math. Anal. Appl. 3 (2006), no. 1, Art. 8, 11 pp. (electronic). | Zbl 1091.30019
Shanmugam, T. N., Sivasuramanian, S. and Srivastava, H. M., Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations, Integral Transforms Spec. Functions 17 (2006), no. 12, 889-899. | Zbl 1104.30015
Shanmugam, T. N., Sivasubramanian, S. and Darus, M., On certain subclasses of functions involving a linear operator, Far East J. Math. Sci. 23 (2006), no. 3, 329-339. | Zbl 1211.30041
Shanmugam, T. N., Sivasubramanian, S. and Owa, S., On sandwich theorems for some subclasses of analytic functions involving a linear operator, to appear in Math. Inequal. Appl. | Zbl 1116.30015
Shanmugam, T. N., Sivasubramanian, S. and Silverman, H., On sandwich theorems for some classes of analytic functions, Int. J. Math. Math. Sci. (2006) Art. ID 29864, 13 pp. | Zbl 1137.30007
Shenan, Gamal M., Tariq, Salim O. and Mousa, Marouf S., A certain class of multivalent prestarlike functions involving the Srivastava-Saigo-Owa fractional integral operator, Kyungpook Math. J. 44 (2004), no. 3, 353-362. | Zbl 1062.30018
Singh, V., On some criteria for univalence and starlikeness, Indian J. Pure Appl. Math. 34 (2003), no. 4, 569-577. | Zbl 1114.30015
Srivastava, H. M., Lashin, A. Y., Some applications of the Briot-Bouquet differential subordination, JIPAM. J. Inequal. Pure Appl. Math. 6 (2005), no. 2, Art. 41, 7 pp. (electronic). | Zbl 1080.30017