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Some properties of certain meromorphic close-to-convex functions. (English) Zbl 1252.30015

Let \(\Sigma\) be the class of functions that are analytic in the punctured open unit disk and let \(g\in\Sigma\) be such that \[ \mathrm{Re}\frac{zf'(z)}{f(z)}<-\frac12 \] for \(|z|<1\). In this paper the authors study a subclass of meromorphic close-to-convex functions \(f\in\Sigma\) satisfying \[ \mathrm{Re}\frac{f'(z)}{g(z)g'(z)}>0 \] and obtain some coefficient inequalities, convolution property, distortion property and radius of meromorphic convexity.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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[1] Srivastava, H.M.; Yang, D.-G.; Xu, N., Some subclasses of meromorphically multivalent functions associated with a linear operator, Appl. math. comput., 195, 11-23, (2008) · Zbl 1175.30028
[2] Chandrashekar, R.; Ali, R.M.; Lee, S.K.; Ravichandran, V., Convolutions of meromorphic multivalent functions with respect to \(n\)-ply points and symmetric conjugate points, Appl. math. comput., 218, 723-728, (2011) · Zbl 1225.30007
[3] Wang, Z.-G.; Jiang, Y.-P.; Srivastava, H.M., Some subclasses of meromorphically multivalent functions associated with the generalized hypergeometric function, Comput. math. appl., 57, 571-586, (2009) · Zbl 1165.30344
[4] Gao, C.-Y.; Zhou, S.-Q., On a class of analytic functions related to the starlike functions, Kyungpook math. J., 45, 123-130, (2005) · Zbl 1085.30015
[5] Kowalczyk, J.; Leś-Bomba, E., On a subclass of close-to-convex functions, Appl. math. lett., 23, 1147-1151, (2010) · Zbl 1193.30018
[6] Şeker, B., On certain new subclass of close-to-convex functions, Appl. math. comput., 218, 1041-1045, (2011) · Zbl 1230.30011
[7] Wang, Z.-G.; Chen, D.-Z., On a subclass of close-to-convex functions, Hacet. J. math. stat., 38, 95-101, (2009) · Zbl 1178.30022
[8] Xu, Q.-H.; Srivastava, H.M.; Li, Z., A certain subclass of analytic and close-to-convex functions, Appl. math. lett., 24, 396-401, (2011) · Zbl 1206.30035
[9] Ali, R.M.; Ravichandran, V., Classes of meromorphic \(\alpha\)-convex functions, Taiwanese J. math., 14, 1479-1490, (2010) · Zbl 1213.30006
[10] Ali, R.M.; Ravichandran, V.; Seenivasagan, N., Subordination and superordination of the liu – srivastava linear operator on meromorphic functions, Bull. malays. math. sci. soc. (2), 31, 193-207, (2008) · Zbl 1151.30016
[11] Ali, R.M.; Ravichandran, V.; Seenivasagan, N., On subordination and superordination of the multiplier transformation for meromorphic functions, Bull. malays. math. sci. soc. (2), 33, 311-324, (2010) · Zbl 1189.30009
[12] Lee, S.K.; Ravichandran, V.; Shamani, S., Coefficient bounds for meromorphic starlike and convex functions, J. inequal. pure appl. math., 10, 1-6, (2009), Article 71 · Zbl 1180.30017
[13] Mohd, M.H.; Ali, R.M.; Keong, L.S.; Ravichandran, V., Subclasses of meromorphic functions associated with convolution, J. inequal. appl., 1-10, (2009), Article ID 190291 · Zbl 1176.30044
[14] Nunokawa, M.; Ahuja, O.P., On meromorphic starlike and convex functions, Indian J. pure appl. math., 32, 1027-1032, (2001) · Zbl 1013.30005
[15] Silverman, H.; Suchithra, K.; Stephen, B.A.; Gangadharan, A., Coefficient bounds for certain classes of meromorphic functions, J. inequal. appl., 1-9, (2008), Article ID 931981 · Zbl 1162.30318
[16] Srivastava, H.M.; Eker, S.S.; Seker, B., Inclusion and neighborhood properties for certain classes of multivalently analytic functions of complex order associated with the convolution structure, Appl. math. comput., 212, 66-71, (2009) · Zbl 1166.30307
[17] Sun, Y.; Kuang, W.-P.; Liu, Z.-H., Subordination and superordination results for the family of jung – kim – srivastava integral operators, Filomat, 24, 69-85, (2010) · Zbl 1265.30095
[18] Wang, Z.-G.; Liu, Z.-H.; Caˇtaş, A., On neighborhoods and partial sums of certain meromorphic multivalent functions, Appl. math. lett., 24, 864-868, (2011) · Zbl 1211.30034
[19] Wang, Z.-G.; Liu, Z.-H.; Sun, Y., Some subclasses of meromorphic functions associated with a family of integral operators, J. inequal. appl., 1-18, (2009), Article ID 931230
[20] Wang, Z.-G.; Liu, Z.-H.; Xiang, R.-G., Some criteria for meromorphic multivalent starlike functions, Appl. math. comput., 218, 1107-1111, (2011) · Zbl 1225.30018
[21] Wang, Z.-G.; Sun, Y.; Zhang, Z.-H., Certain classes of meromorphic multivalent functions, Comput. math. appl., 58, 1408-1417, (2009) · Zbl 1189.30045
[22] Yuan, S.-M.; Liu, Z.-M.; Srivastava, H.M., Some inclusion relationships and integral-preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators, J. math. anal. appl., 337, 505-515, (2008) · Zbl 1129.30020
[23] Zhou, J.-R.; Liu, Z.-H.; Wang, Z.-G., Some properties of certain class of integral operators, J. inequal. appl., 1-10, (2011), Article ID 531540
[24] Clunie, J., On meromorphic schlicht functions, J. lond. math. soc., 34, 215-216, (1959) · Zbl 0087.07704
[25] Goodman, A.W., Univalent functions, vol. 1, (1983), Polygonal Publishing House Washington, NJ · Zbl 1041.30500
[26] Pommerenke, Ch., On meromorphic starlike functions, Pacific J. math., 13, 221-235, (1963) · Zbl 0116.05701
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