×

Certain classes of meromorphic multivalent functions. (English) Zbl 1189.30045

Summary: We introduce and investigate two new classes of meromorphic multivalent functions. Such results as subordination properties, coefficient inequalities, convolution properties and integral representations are proved. Several sufficient conditions for meromorphic multivalent starlikeness and convexity are also derived.

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
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Nunokawa, M.; Ahuja, O. P., On meromorphic starlike and convex functions, Indian J. Pure Appl. Math., 32, 1027-1032 (2001) · Zbl 1013.30005
[2] R.M. Ali, V. Ravichandran, Classes of meromorphic \(\alpha \); R.M. Ali, V. Ravichandran, Classes of meromorphic \(\alpha \) · Zbl 1213.30006
[3] Ali, R. M.; Ravichandran, V.; Seenivasagan, N., Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions, Bull. Malays. Math. Sci. Soc., 31, 193-207 (2008) · Zbl 1151.30016
[4] Aouf, M. K., Certain subclasses of meromorphically multivalent functions associated with generalized hypergeometric function, Comput. Math. Appl., 55, 494-509 (2008) · Zbl 1155.30306
[5] Aouf, M. K., Argument estimates of certain meromorphically multivalent functions associated with generalized hypergeometric function, Appl. Math. Comput., 206, 772-780 (2008) · Zbl 1171.33004
[6] Aouf, M. K., Certain subclasses of meromorphically \(p\)-valent functions with positive or negative coefficients, Math. Comput. Modelling, 47, 997-1008 (2008) · Zbl 1144.30302
[7] Aouf, M. K., A class of meromorphic multivalent functions with positive coefficients, Taiwanese J. Math., 12, 2517-2533 (2008) · Zbl 1170.30301
[8] Aouf, M. K.; El-Ashwah, R. M., Properties of certain subclasses of meromorphic functions with positive coefficients, Math. Comput. Modelling, 49, 868-879 (2009) · Zbl 1165.30311
[9] Aouf, M. K.; Silverman, H., Partial sums of certain meromorphic \(p\)-valent functions, J. Inequal. Pure Appl. Math., 7, 1-7 (2006), Article 119 (electronic) · Zbl 1131.30307
[10] Aouf, M. K.; Yassen, M. F., On certain classes of meromorphically multivalent functions associated with the generalized hypergeometric function, Comput. Math. Appl., 58, 449-463 (2009) · Zbl 1189.30011
[11] Cho, N. E., On certain subclasses of meromorphically multivalent convex functions, J. Math. Anal. Appl., 193, 255-263 (1995) · Zbl 0839.30014
[12] Cho, N. E.; Kim, I. H., Inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 187, 115-121 (2007) · Zbl 1119.30006
[13] Cho, N. E.; Kwon, O. S.; Owa, S.; Srivastava, H. M., A class of integral operators preserving subordination and superordination for meromorphic functions, Appl. Math. Comput., 193, 463-474 (2007) · Zbl 1193.30032
[14] Cho, N. E.; Kwon, O. S.; Srivastava, H. M., Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations, J. Math. Anal. Appl., 300, 505-520 (2004) · Zbl 1058.30012
[15] Cho, N. E.; Kwon, O. S.; Srivastava, H. M., Inclusion relationships for certain subclasses of meromorphic functions associated with a family of multiplier transformations, Integral Transforms Spec. Funct., 16, 647-659 (2005) · Zbl 1096.30008
[16] Cho, N. E.; Noor, K. I., Inclusion properties for certain classes of meromorphic functions associated with the Choi-Saigo-Srivastava operator, J. Math. Anal. Appl., 320, 779-786 (2006) · Zbl 1102.30013
[17] Cho, N. E.; Owa, S., On certain classes of meromorphically \(p\)-valent starlike functions, Appl. Math. Lett., 7, 25-28 (1994) · Zbl 0804.30011
[18] Cho, N. E.; Owa, S., Certain classes of meromorphically \(p\)-valent starlike functions, Appl. Math. Lett., 7, 85-87 (1994) · Zbl 0974.30528
[19] El-Ashwah, R. M., Some properties of certain subclasses of meromorphically multivalent functions, Appl. Math. Comput., 204, 824-832 (2008) · Zbl 1155.30316
[20] El-Ashwah, R. M.; Aouf, M. K., Hadamard product of certain meromorphic starlike and convex functions, Comput. Math. Appl., 57, 1102-1106 (2009) · Zbl 1186.30014
[21] Frasin, B. A.; Murugusundaramoorthy, G., New subclasses of meromorphic \(p\)-valent functions, J. Inequal. Pure Appl. Math., 6, 1-10 (2005), Article 68 (electronic) · Zbl 1086.30014
[22] Gordji, M. E.; Ebadian, A., Convexity of a family of meromorphically univalent functions by using two fixed points, Appl. Math. Lett., 22, 1200-1204 (2009) · Zbl 1173.30307
[23] Irmak, H., Some applications of Hadamard convolution to multivalently analytic and multivalently meromorphic functions, Appl. Comput. Math., 187, 207-214 (2007) · Zbl 1122.30007
[24] Joshi, S. B.; Srivastava, H. M., A certain family of meromorphically multivalent functions, Comput. Math. Appl., 38, 201-211 (1999) · Zbl 0959.30010
[25] Kulkarni, S. R.; Naik, U. H.; Srivastava, H. M., A certain class of meromorphically \(p\)-valent quasi-convex functions, Panamer. Math. J., 8, 57-64 (1998) · Zbl 0957.30013
[26] Liu, J.-L., Some properties of certain meromorphically multivalent functions, Appl. Math. Comput., 210, 136-140 (2009) · Zbl 1162.30314
[27] Liu, J.-L.; Owa, S., On certain meromorphic \(p\)-valent functions, Taiwanese J. Math., 2, 107-110 (1998) · Zbl 0909.30012
[28] Liu, J.-L.; Srivastava, H. M., A linear operator and associated families of meromorphically multivalent functions, J. Math. Anal. Appl., 259, 566-581 (2001) · Zbl 0997.30009
[29] Liu, J.-L.; Srivastava, H. M., Some convolution conditions for starlikeness and convexity of meromorphically multivalent functions, Appl. Math. Lett., 16, 13-16 (2003) · Zbl 1057.30013
[30] Liu, J.-L.; Srivastava, H. M., Classes of meromorphically multivalent functions associated with the generalized hypergeometric function, Math. Comput. Modelling, 39, 21-34 (2004) · Zbl 1049.30008
[31] Liu, J.-L.; Srivastava, H. M., Subclasses of meromorphically multivalent functions associated with a certain linear operator, Math. Comput. Modelling, 39, 35-44 (2004) · Zbl 1049.30009
[32] Mohd, M. H.; Ali, R. M.; Keong, L. S.; Ravichandran, V., Subclasses of meromorphic functions associated with convolution, J. Inequal. Appl., 2009, 1-10 (2009), Article ID 190291 · Zbl 1176.30044
[33] Nasser, M.; Darus, M., Certain classes of meromorphic \(p\)-valent functions with positive coefficients, Tamkang J. Math., 37, 251-260 (2006) · Zbl 1167.30308
[34] Owa, S.; Pascu, N. N., Coefficient inequalities for certain classes of meromorphically starlike and meromorphically convex functions, J. Inequal. Pure Appl. Math., 4, 1-6 (2003), Article 17 (electronic) · Zbl 1025.30008
[35] Piejko, K.; Sokól, J., Subclasses of meromorphic functions associated with the Cho-Kwon-Srivastava operator, J. Math. Anal. Appl., 337, 1261-1266 (2008) · Zbl 1200.30021
[36] Raina, R. K.; Srivastava, H. M., A new class of meromorphically multivalent functions with applications to generalized hypergeometric functions, Math. Comput. Modelling, 43, 350-356 (2006) · Zbl 1140.30007
[37] Ravichandran, V.; Kumar, S. S.; Darus, M., On a subordination theorem for a class of meromorphic functions, J. Inequal. Pure Appl. Math., 5, 1-4 (2004), Article 8 (electronic) · Zbl 1049.30015
[38] Ravichandran, V.; Kumar, S. S.; Subramanian, K. G., Convolution conditions for spirallikeness and convex spirallikeness of certain meromorphic \(p\)-valent functions, J. Inequal. Pure Appl. Math., 5, 1-7 (2004), Article 11 (electronic) · Zbl 1062.30017
[39] Silverman, H.; Suchithra, K.; Stephen, B. A.; Gangadharan, A., Coefficient bounds for certain classes of meromorphic functions, J. Inequal. Appl., 2008, 1-9 (2008), Article ID 931981 · Zbl 1162.30318
[40] Srivastava, H. M.; Hossen, H. M.; Aouf, M. K., A unified presentation of some classes of meromorphically multivalent functions, Comput. Math. Appl., 38, 63-70 (1999) · Zbl 0978.30011
[41] (Srivastava, H. M.; Owa, S., Current Topics in Analytic Function Theory (1992), Worldscientific: Worldscientific Singapore, New York, London, Hongkong) · Zbl 0976.00007
[42] Srivastava, H. M.; Patel, J., Certain subclasses of meromorphically multivalent functions involving a family of linear operators, Southeast Asian Bull. Math., 30, 123-140 (2006) · Zbl 1110.30010
[43] Srivastava, H. M.; Patel, J., Applications of differential subordination to certain subclasses of meromorphically multivalent functions, J. Inequal. Pure Appl. Math., 6, 1-15 (2005), Article 88 (electronic) · Zbl 1096.30012
[44] 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
[45] 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
[46] Yang, D.-G.; Liu, J.-L., A class of meromorphically multivalent functions defined by means of a linear operator, Appl. Math. Comput., 204, 862-871 (2008) · Zbl 1155.30342
[47] 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.