Some properties for meromorphic functions associated with integral operators
Tóm tắt
In the present paper we aim at proving some subordinations properties for meromorphic functions analytic in the punctured unit disc
$$\Delta ^*=\{z:0<|z|<1\}$$
with a simple pole at the origin. The functions under investigation are associated with two integral operators
$$\mathcal {P}_\sigma ^\gamma$$
and
$$\mathcal {Q}_\sigma ^\gamma$$
(see Lashin in Comput Math Appl 59:524–531, 2010,
https://doi.org/10.1016/j.camwa.2009.06.015
). Several other results and numerical examples are also obtained.
Tài liệu tham khảo
Lashin, A.Y.: On certain subclasses of meromorphic functions associated with certain integral operators. Comput. Math. Appl. 59, 524–531 (2010). https://doi.org/10.1016/j.camwa.2009.06.015
Duren P.L.: Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259. Springer, New York (1983)
Bulboacâ, T.: Differential Subordinations and Superordinations: Recent Results. House of Scientific Book Publishing, Cluj-Napoca (2005)
Miller, S.S., Mocanu, P.T.: Differential Subordinations: Theory and Applications. Marcel Dekker Incorporated, New York (2000)
Kumar, V., Shukla, S.L.: Certain integrals for classes of p-valent meromorphic functions. Bull. Austral. Math. Soc. 25, 35–97 (1982). https://doi.org/10.1017/S0004972700005062
Hallenbeck, D.J., Ruscheweyh, S.T.: Subordination by convex functions. Proc. Am. Math. Soc. 52, 191–195 (1975). https://doi.org/10.1090/S0002-9939-1975-0374403-3
Miller, S.S., Mocanu, P.T.: Differential subordination and univalent functions. Michigan Math. J. 28, 157–171 (1981). https://doi.org/10.1307/mmj/1029002507
Abramowitz, M., Stegun, I.A.: Hand Book of Mathematical functions. Dover Publications, Inc., New York (1971)
Whittaker, E.T., Watson, G.N.: A Course on Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With An Account of the Principal Transcendental Functions, 4th edn. Cambridge University Press, Cambridge (1927)