×
Noor, Khalida Inayat; Amber, Fiaz

On certain classes of meromorphic functions associated with conic domains. (English) Zbl 1235.30010

Abstr. Appl. Anal. 2012, Article ID 801601, 13 p. (2012).
Summary: Making use of the concept of \(k\)-uniformly bounded boundary rotation and Ruscheweyh differential operator, we introduce some new classes of meromorphic functions in the punctured unit disc. Convolution technique and principle of subordination are used to investigate these classes. Inclusion results, generalized Bernardi integral operator, and rate of growth of coefficients are studied. Some interesting consequences are also derived from the main results.

Cited in 2 Documents

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
PDFBibTeX XMLCite
\textit{K. I. Noor} and \textit{F. Amber}, Abstr. Appl. Anal. 2012, Article ID 801601, 13 p. (2012; Zbl 1235.30010)
Full Text: DOI
OA License

References:

[1] A. W. Goodman, Univalent Functions, vol. 2, Mariner Publishing, Tampa, Fla, USA, 1983. · Zbl 1041.30501
[2] M. S. Robertson, “Convolutions of schlicht functions,” Proceedings of the American Mathematical Society, vol. 13, pp. 585-589, 1962. · Zbl 0114.27904 · doi:10.2307/2034830
[3] S. Kanas, “Techniques of the differential subordination for domains bounded by conic sections,” International Journal of Mathematics and Mathematical Sciences, no. 38, pp. 2389-2400, 2003. · Zbl 1130.30307 · doi:10.1155/S0161171203302212
[4] K. I. Noor, “On a generalization of uniformly convex and related functions,” Computers & Mathematics with Applications, vol. 61, no. 1, pp. 117-125, 2011. · Zbl 1207.30023 · doi:10.1016/j.camwa.2010.10.038
[5] B. Pinchuk, “Functions of bounded boundary rotation,” Israel Journal of Mathematics, vol. 10, pp. 7-16, 1971. · Zbl 0224.30024 · doi:10.1007/BF02771515
[6] J. Noonan, “Meromorphic functions of bounded boundary rotation,” The Michigan Mathematical Journal, vol. 18, pp. 343-352, 1971. · Zbl 0221.30016 · doi:10.1307/mmj/1029000739
[7] K. I. Noor, “Higher order close-to-convex functions,” Mathematica Japonica, vol. 37, no. 1, pp. 1-8, 1992. · Zbl 0758.30010 · doi:10.1155/S016117129200036X
[8] S. S. Miller, “Differential inequalities and Caratheodory functions,” Bulletin of the American Mathematical Society, vol. 81, pp. 79-81, 1975. · Zbl 0302.30003 · doi:10.1090/S0002-9904-1975-13643-3
[9] H. Yoshikawa and T. Yoshikai, “Some notes on Bazilevic functions,” The Journal of the London Mathematical Society, vol. 20, no. 1, pp. 79-85, 1979. · Zbl 0409.30018 · doi:10.1112/jlms/s2-20.1.79
[10] Ch. Pommerenke, “On the coefficients of close-to-convex functions,” The Michigan Mathematical Journal, vol. 9, pp. 259-269, 1962. · Zbl 0105.05905 · doi:10.1307/mmj/1028998726
[11] S. K. Bajpai, “A note on a class of meromorphic univalent functions,” Academie de la Republique Populaire Roumaine, vol. 22, no. 3, pp. 295-297, 1977. · Zbl 0354.30006
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.