zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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:
30C45Special classes of univalent and multivalent functions
30C50Coefficient problems for univalent and multivalent functions
30C80Maximum principle; Schwarz’s lemma, Lindelöf principle, etc. (one complex variable)
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 α-convex functions, Taiwanese J. Math. (in press)
[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 · doi:http://math.usm.my/bulletin/pdf/v31n2/v31n2p9.pdf
[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 · doi:10.1016/j.camwa.2007.05.005
[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 · doi:10.1016/j.amc.2008.09.046
[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 · doi:10.1016/j.mcm.2007.04.018
[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 · doi:10.1016/j.mcm.2008.04.013
[9]Aouf, M. K.; Silverman, H.: Partial sums of certain meromorphic p-valent functions, J. inequal. Pure appl. Math. 7, 1-7 (2006) · Zbl 1131.30307 · doi:emis:journals/JIPAM/article736.html
[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 · doi:10.1016/j.camwa.2009.04.013
[11]Cho, N. E.: On certain subclasses of meromorphically multivalent convex functions, J. math. Anal. appl. 193, 255-263 (1995) · Zbl 0839.30014 · doi:10.1006/jmaa.1995.1233
[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 · doi:10.1016/j.amc.2006.08.109
[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 · doi:10.1016/j.amc.2007.03.084
[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 · doi:10.1016/j.jmaa.2004.07.001
[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 · doi:10.1080/10652460500389073
[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 · doi:10.1016/j.jmaa.2005.07.045
[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 · doi:10.1016/0893-9659(94)90107-4
[18]Cho, N. E.; Owa, S.: Certain classes of meromorphically p-valent starlike functions, Appl. math. Lett. 7, 85-87 (1994) · Zbl 0974.30528 · doi:10.1016/0893-9659(94)90059-0
[19]El-Ashwah, R. M.: Some properties of certain subclasses of meromorphically multivalent functions, Appl. math. Comput. 204, 824-832 (2008) · Zbl 1155.30316 · doi:10.1016/j.amc.2008.07.032
[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 · doi:10.1016/j.camwa.2008.07.044
[21]Frasin, B. A.; Murugusundaramoorthy, G.: New subclasses of meromorphic p-valent functions, J. inequal. Pure appl. Math. 6, 1-10 (2005) · 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 · doi:10.1016/j.aml.2009.01.030
[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 · doi:10.1016/j.amc.2006.08.117
[24]Joshi, S. B.; Srivastava, H. M.: A certain family of meromorphically multivalent functions, Comput. math. Appl. 38, 201-211 (1999) · Zbl 0959.30010 · doi:10.1016/S0898-1221(99)00194-7
[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 · doi:10.1016/j.amc.2008.12.070
[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 · doi:10.1006/jmaa.2000.7430
[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 · doi:10.1016/S0893-9659(02)00138-6
[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 · doi:10.1016/S0895-7177(04)90503-1
[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 · doi:10.1016/S0895-7177(04)90504-3
[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) · Zbl 1176.30044 · doi:10.1155/2009/190291
[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) · Zbl 1025.30008 · doi:http://jipam-old.vu.edu.au/v4n1/
[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 · doi:10.1016/j.jmaa.2007.04.030
[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 · doi:10.1016/j.mcm.2005.09.031
[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) · 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) · 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)
[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 · doi:10.1016/S0898-1221(99)00285-0
[41], Current topics in analytic function theory (1992)
[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) · 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 · doi:10.1016/j.amc.2007.04.065
[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 · doi:10.1016/j.camwa.2008.01.038
[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 · doi:10.1016/j.amc.2008.07.028
[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 · doi:10.1016/j.jmaa.2007.04.018