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Starlikeness of general integral operator for meromorphic multivalent functions. (English) Zbl 1268.30019
Summary: We introduce a new integral operator $$\cal I^p_{\gamma, \delta}(f_1, \dots, f_n)$$ for meromorphic multivalent functions. The starlikeness condition of this integral operator is determined. Several special cases are also discussed in the form of corollaries.
30C45Special classes of univalent and multivalent functions
Full Text: DOI
[1] B. A. Frasin, “Order of convexity and univalency of general integral operator,” Journal of the Franklin Institute, vol. 348, no. 6, pp. 1013-1019, 2011. · Zbl 1220.30021 · doi:10.1016/j.jfranklin.2011.03.006
[2] S. Bulut and P. Goswami, “Starlikeness properties of general integral operator for meromorphic univalent functions,” Southeast Asian Bulletin of Mathematics, vol. 37, 2013. · Zbl 1299.30019
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[5] A. Mohammed and M. Darus, “New criteria for meromorphic functions,” International Journal of Applied Mathematics & Statistics, vol. 33, no. 3, 2013. · Zbl 1289.30084
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[8] Z.-G. Wang, Z.-H. Liu, and R.-G. Xiang, “Some criteria for meromorphic multivalent starlike functions,” Applied Mathematics and Computation, vol. 218, no. 3, pp. 1107-1111, 2011. · Zbl 1225.30018 · doi:10.1016/j.amc.2011.03.079
[9] Z.-G. Wang, Y. Sun, and N. Xu, “Some properties of certain meromorphic close-to-convex functions,” Applied Mathematics Letters, vol. 25, no. 3, pp. 454-460, 2012. · Zbl 1252.30015 · doi:10.1016/j.aml.2011.09.035
[10] Z.-G. Wang, Y. Sun, and Z.-H. Zhang, “Certain classes of meromorphic multivalent functions,” Computers and Mathematics with Applications, vol. 58, no. 7, pp. 1408-1417, 2009. · Zbl 1189.30045 · doi:10.1016/j.camwa.2009.07.020
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[12] A. Mohammed and M. Darus, “Starlikeness properties of a new integral operator for meromorphic functions,” Journal of Applied Mathematics, vol. 2011, Article ID 804150, 8 pages, 2011. · Zbl 1223.30005 · doi:10.1155/2011/804150