A Differential Operator and its Applications to Certain Multivalently Analytic Functions

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

In the present paper, the authors obtain some interesting properties of (ordinary) differential operators. Several useful consequences associated with the main results are also considered.

Keywords:

Open unit disk, Multivalently analytic function, Multivalently starlike, Multivalently convex, Multivalently close-to-convex (Ordinary) Differential operator, 2000 AMS Classification: 30 C 45,

PDF

___

Chen, M. P., Irmak, H. and Srivastava, H. M. Some families multivalently analytic functions with negative coefficients, J. Math. Anal. Appl. 214 (2), 674–690, 1997.
Duren, P. L. Univalent Functions, Grundlehren der Mathematischen Wissenschaften 259 (Springer-Verlag, New York, Berlin, Heidelberg, and Tokyo, 1983).
Goodman, A. W. Univalent Functions, Vols. I and II (Polygonal Publishing House, Wash- ington, New Jersey, 1983).
Irmak, H., Cho, N. E., C¸ etin, ¨O. F. and Raina, R. K. Certain inequalities involving meromor- phically multivalent functions, Hacet. Bull. Nat. Sci. Eng. Ser. B 30, 39–43, 2001.
Irmak, H., Lee, S. H. and Cho, N. E. Some multivalently starlike functions with negative coefficients and their subclasses defined by using a differential operator, Kyungpook Math. J. 37 (1), 43–51, 1997.
Irmak, H. A class of p-valently analytic functions with positive coefficients, Tamkang J. Math. 27(4), 315–322, 1995.
Jack, I. S. Functions starlike and convex of order α, J. London Math. Soc. 3, 469–474, 1971.
Miller, S. S. and Mocanu, P. T. Second order differential inequalities in the complex palne, J. Math. Anal. Appl. 65, 289–305, 1978.
Srivastava, H. M. and Owa, S. (Editors), Current Topics in Analytic Function Theory (World Scientific Publishing Company, Singapore, New Jersey, London, and Hong Kong, 1992).