×
Liu, Jin-Lin; Srivastava, H. M.

Some convolution conditions for starlikeness and convexity of meromorphically multivalent functions. (English) Zbl 1057.30013

Appl. Math. Lett. 16, No. 1, 13-16 (2003).
Summary: By making use of the Hadamard product (or convolution), the authors derive necessary and sufficient conditions for a suitably normalized meromorphically \(p\)-valent function to be in the familiar classes of meromorphic \(p\)-valently starlike and meromorphic \(p\)-valently convex functions in the punctured unit disk.

Cited in 12 Documents

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

Hadamard product (or convolution); Meromorphic functions; multivalentfunctions; analytic functions; starlike functions; convex functions
PDF BibTeX XML Cite
\textit{J.-L. Liu} and \textit{H. M. Srivastava}, Appl. Math. Lett. 16, No. 1, 13--16 (2003; Zbl 1057.30013)
Full Text: DOI

References:

[1] Duren, P. L., Univalent functions, (Grundlehren der Mathematischen Wissenschaften, Bd., Volume 259 (1983), Springer-Verlag: Springer-Verlag New York) · Zbl 0398.30010
[2] Aouf, M. K., New criteria for multivalent meromorphic starlike functions of order alpha, (Proc. Japan Acad. Ser. A Math. Sci., 69 (1993)), 66-70 · Zbl 0786.30011
[3] Aouf, M. K.; Hossen, H. M., New criteria for meromorphic \(p- valent\) starlike functions, Tsukuba J. Math., 17, 481-486 (1993) · Zbl 0804.30012
[4] Aouf, M. K.; Srivastava, H. M., A new criterion for meromorphically \(p- valent\) convex functions of order alpha, Math. Sci. Res. Hot-Line, 1, 8, 7-12 (1997) · Zbl 0893.30011
[5] Cho, N. E.; Owa, S., (Owa, S., On certain classes of meromorphically \(p- valent\) starlike functions. On certain classes of meromorphically \(p- valent\) starlike functions, New Developments in Univalent Function Theory, Volume 821 (1993), Research Institute for Mathematical Sciences, Kyoto University: Research Institute for Mathematical Sciences, Kyoto University Kyoto), 159-165, Kyoto; August 4-7, 1992, Sūrikaisekikenkyūsho Kōkyūroku
[6] Joshi, S. B.; Srivastava, H. M., A certain family of meromorphically multivalent functions, Computers Math. Appl., 38, 3/4, 201-211 (1999) · Zbl 0959.30010
[7] Kulkarni, S. R.; Naik, U. H.; Srivastava, H. M., A certain class of meromorphically \(p- valent\) quasi-convex functions, Pan Amer. Math. J., 8, 1, 57-64 (1998) · Zbl 0957.30013
[8] 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
[9] Mogra, M. L., Meromorphic multivalent functions with positive coefficients I and II, Math. Japon., 35, 1089-1098 (1990) · Zbl 0718.30009
[10] Owa, S.; Darwish, H. E.; Aouf, M. K., Meromorphic multivalent functions with positive and fixed second coefficients, Math. Japon., 46, 231-236 (1997) · Zbl 0895.30009
[11] Srivastava, H. M.; Hossen, H. M.; Aouf, M. K., A unified presentation of some classes of meromorphically multivalent functions, Computers Math. Appl., 38, 11/12, 63-70 (1999) · Zbl 0978.30011
[12] Uralegaddi, B. A.; Somanath, C., Certain classes of meromorphic multivalent functions, Tamkang J. Math., 23, 223-231 (1992) · Zbl 0769.30012
[13] Yang, D.-G., On new subclasses of meromorphic \(p- valent\) functions, J. Math. Res. Exposition, 15, 7-13 (1995) · Zbl 1108.30309
[14] (Srivastava, H. M.; Owa, S., Current Topics in Analytic Function Theory (1992), World Scientific: World Scientific Singapore) · Zbl 0976.00007
[15] Silverman, H.; Silvia, E. M.; Telage, D., Convolution conditions for convexity, starlikeness and spiral-likeness, Math. Zeitschr., 162, 125-130 (1978) · Zbl 0369.30004
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.