On a new criterion for meromorphic starlike functions. (English) Zbl 1469.30034

Summary: The main purpose of this paper is to derive a new criterion for meromorphic starlike functions of order \(\alpha\).


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
Full Text: DOI


[1] Miller, S. S.; Mocanu, P. T.; Oros, G., On a starlikeness condition for meromorphic functions, Mathematica, 41, 2, 221-225, (1999) · Zbl 1027.30500
[2] Catas, A., Some simple criteria of starlikeness for meromorphic functions, Filomat, 22, 2, 109-113, (2008) · Zbl 1224.30040
[3] Ali, R. M.; Ravichandran, V., Classes of meromorphic α-convex functions, Taiwanese Journal of Mathematics, 14, 4, 1479-1490, (2010) · Zbl 1213.30006
[4] Catas, A., A note on meromorphic \(m\)-valent starlike functions, Journal of Mathematical Inequalities, 4, 4, 601-607, (2010) · Zbl 1206.30013
[5] Kwon, O. S.; Cho, N. E., A class of nonlinear integral operators preserving double subordinations, Abstract and Applied Analysis, 2008, (2008) · Zbl 1152.30311
[6] Noor, K. I.; Amber, F., On certain classes of meromorphic functions associated with conic domains, Abstract and Applied Analysis, 2012, (2012) · Zbl 1235.30010
[7] Nunokawa, M.; Ahuja, O. P., On meromorphic starlike and convex functions, Indian Journal of Pure and Applied Mathematics, 32, 7, 1027-1032, (2001) · Zbl 1013.30005
[8] Nunokawa, M.; Owa, S.; Uyanik, N.; Shiraishi, H., Sufficient conditions for starlikeness of order α for meromorphic functions, Mathematical and Computer Modelling, 55, 3-4, 1245-1250, (2012) · Zbl 1255.30023
[9] Tang, H.; Deng, G.-T.; Li, S.-H., On a certain new subclass of meromorphic close-to-convex functions, Journal of Inequalities and Applications, 2013, article 164, 1-6, (2013) · Zbl 1296.30025
[10] Wang, Z.-G.; Liu, Z.-H.; Xiang, R.-G., Some criteria for meromorphic multivalent starlike functions, Applied Mathematics and Computation, 218, 3, 1107-1111, (2011) · Zbl 1225.30018
[11] Wang, Z.-G.; Sun, Y.; Xu, N., Some properties of certain meromorphic close-to-convex functions, Applied Mathematics Letters, 25, 3, 454-460, (2012) · Zbl 1252.30015
[12] Wang, Z.-G.; Srivastava, H. M.; Yuan, S.-M., Some basic properties of certain subclasses of meromorphically starlike functions, Journal of Inequalities and Applications, 2014, article 29, 1-13, (2014) · Zbl 1307.30039
[13] Hallenbeck, D. J.; Ruscheweyh, S., Subordination by convex functions, Proceedings of the American Mathematical Society, 52, 191-195, (1975) · Zbl 0311.30010
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.