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Starlikeness properties of a new integral operator for meromorphic functions. (English) Zbl 1223.30005
Summary: We define here an integral operator $\Cal H_{\gamma_{1},\dots,\gamma_{n}}$ for meromorphic functions in the punctured open unit disk. Several starlikeness conditions for the integral operator $\Cal H_{\gamma_{1},\dots,\gamma_{n}}$ are derived.

30C45Special classes of univalent and multivalent functions
Full Text: DOI
[1] D. Breaz, S. Owa, and N. Breaz, “A new integral univalent operator,” Acta Universitatis Apulensis, no. 16, pp. 11-16, 2008. · Zbl 1212.30031 · eudml:233764
[2] S. S. Miller and P. T. Mocanu, “Differential subordinations and univalent functions,” The Michigan Mathematical Journal, vol. 28, no. 2, pp. 157-172, 1981. · Zbl 0439.30015 · doi:10.1307/mmj/1029002507
[3] A. Mohammed and M. Darus, “New criteria for meromorphic functions,” Submitted. · Zbl 1224.30062
[4] A. Mohammed and M. Darus, “New properties for certain integral operators,” International Journal of Mathematical Analysis, vol. 4, no. 41-44, pp. 2101-2109, 2010. · Zbl 1218.30043 · http://www.m-hikari.com/ijma/ijma-2010/ijma-41-44-2010/index.html
[5] A. Mohammed and M. Darus, “A new integral operator for meromorphic functions,” Acta Universitatis Apulensis, no. 24, pp. 231-238, 2010. · Zbl 1224.30062 · eudml:230102
[6] N. Breaz, D. Breaz, and M. Darus, “Convexity properties for some general integral operators on uniformly analytic functions classes,” Computers and Mathematics with Applications, vol. 60, no. 12, pp. 3105-3107, 2010. · Zbl 1207.41012 · doi:10.1016/j.camwa.2010.10.012