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Subordination and superordination of a certain integral operator on meromorphic functions. (English) Zbl 1198.30010

Summary: Using the methods of differential subordination and superordination, sufficient conditions on the integral operator of meromorphic functions in the punctured unit disk for obtaining, respectively, the best dominant and the best subordinant are determined. New Sandwich-type results are also obtained.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
45P05 Integral operators
30Dxx Entire and meromorphic functions of one complex variable, and related topics
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[1] Miller, S. S.; Mocanu, P. T., (Differential Subordinations: Theory and Applications. Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, vol. 225 (2000), Marcel Dekker: Marcel Dekker New York, Basel) · Zbl 0954.34003
[2] Miller, S. S.; Mocanu, P. T., Subordinants of differential superordinations, Complex Variables Theory Appl., 48, 10, 815-826 (2003) · Zbl 1039.30011
[3] Aqlan, E.; Jahangiri, J. M.; Kulkarni, S. R., Certain integral operators applied to \(p\)-valent functions, J. Nat. Geom., 24, 111-120 (2003) · Zbl 1040.30007
[4] Ali, R. M.; Ravichandran, V.; Seenivasagan, N., Subordination and superordination of Liu-Srivastava linear operator on meromorphic functions, Bull. Malays. Math. Sci. Soc. (2), 31, 2, 193-207 (2008) · Zbl 1151.30016
[5] Magesh, N.; Murugusundaramoorthy, G., Differential Subordinations and superordinations of integral operator on meromorphic functions, Math. Sci. Res. J., 13, 3, 68-79 (2009) · Zbl 1180.30018
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