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Certain subclasses of multivalent analytic functions involving the generalized Srivastava-Attiya operator. (English) Zbl 1187.30024

Summary: By making use of the principle of subordination between analytic functions and the generalized Srivastava-Attiya operator, we introduce and investigate some new subclasses of multivalent analytic functions. Such results as inclusion relationships and integral-preserving properties involving these subclasses are proved. Several subordination and superordination results associated with this operator are also derived.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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[1] DOI: 10.1016/j.jmaa.2003.12.026 · Zbl 1059.30006 · doi:10.1016/j.jmaa.2003.12.026
[2] DOI: 10.1080/10652460601135342 · Zbl 1109.30022 · doi:10.1080/10652460601135342
[3] DOI: 10.1016/S0022-247X(02)00500-0 · Zbl 1035.30004 · doi:10.1016/S0022-247X(02)00500-0
[4] DOI: 10.1016/j.amc.2004.12.004 · Zbl 1082.11052 · doi:10.1016/j.amc.2004.12.004
[5] Eenigenburg P., General Mathematics 29 pp 567– (1984)
[6] DOI: 10.1016/j.jmaa.2004.05.040 · Zbl 1106.11034 · doi:10.1016/j.jmaa.2004.05.040
[7] DOI: 10.1016/j.camwa.2004.10.041 · Zbl 1085.30014 · doi:10.1016/j.camwa.2004.10.041
[8] DOI: 10.1080/10652460600926907 · Zbl 1184.11005 · doi:10.1080/10652460600926907
[9] DOI: 10.1016/S0096-3003(03)00746-X · Zbl 1078.11054 · doi:10.1016/S0096-3003(03)00746-X
[10] DOI: 10.1080/10652460600926923 · Zbl 1172.11026 · doi:10.1080/10652460600926923
[11] DOI: 10.1080/10652460802357687 · Zbl 1151.30004 · doi:10.1080/10652460802357687
[12] DOI: 10.1016/j.jmaa.2005.01.020 · Zbl 1076.33006 · doi:10.1016/j.jmaa.2005.01.020
[13] Ma, W. C. and Minda, D. Proceedings of the Conference on Complex Analysis, Tianjin, 1992; in Conference Proceedings and Lecture Notes in Analysis, I. Cambridge, MA. A unified treatment of some special classes of univalent functions, pp.157–169. International Press. · Zbl 0823.30007
[14] DOI: 10.1307/mmj/1029002507 · Zbl 0439.30015 · doi:10.1307/mmj/1029002507
[15] DOI: 10.1080/10652460701318111 · Zbl 1115.30013 · doi:10.1080/10652460701318111
[16] DOI: 10.1155/S0161171287000310 · Zbl 0637.30012 · doi:10.1155/S0161171287000310
[17] DOI: 10.1016/S0893-9659(01)00094-5 · Zbl 1038.30011 · doi:10.1016/S0893-9659(01)00094-5
[18] Prajapat J. K., J. Math. Inequal. 3 pp 129– (2009) · Zbl 1160.30325 · doi:10.7153/jmi-03-13
[19] DOI: 10.1080/10652460701542074 · Zbl 1130.30003 · doi:10.1080/10652460701542074
[20] DOI: 10.1080/10652460701208577 · Zbl 1112.30007 · doi:10.1080/10652460701208577
[21] Srivastava H. M., Series Associated with the Zeta and Related Functions (2001) · Zbl 1014.33001 · doi:10.1007/978-94-015-9672-5
[22] Srivastava H. M., J. Inequal. Pure Appl. Math. 6 pp 1– (2005)
[23] Srivastava H. M., Current Topics in Analytic Function Theory (1992) · Zbl 0976.00007 · doi:10.1142/1628
[24] DOI: 10.1016/j.jmaa.2005.08.060 · Zbl 1102.30015 · doi:10.1016/j.jmaa.2005.08.060
[25] DOI: 10.1080/10652460701635456 · Zbl 1138.30016 · doi:10.1080/10652460701635456
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