Some remarks on multivalent functions of higher-order derivatives

Abstract

Two subclasses G_{p,q}(β) and J_{p,q}(α,β,f(z)) of p-valently starlike functions of higher-order derivatives are introduced. The object of the present paper is to derive some properties for the classes G_{p,q}(β) and J_{p,q}(α,β,f(z)). The results obtained generalize the related works of some authors and some other new results are obtained.

Downloads

Download data is not yet available.

Author Biographies

M. K. Aouf, Mansoura University

Department of Mathematics Faculty of Science

Abdel Moneim Lashin, Mansoura University

Department of Mathematics Faculty of Science

References

Aouf, M. K., A generalization of mulivalent functions with negative coefficients, J. Korean Math. soc. 25, no. 1, 53-66, (1988).

Aouf, M. K., Certain subclasses of p-valent functions defined by using a differential operator, Appl. Math. Comput. 206, 867-875, (2008). DOI: https://doi.org/10.1016/j.amc.2008.09.048

Aouf, M. K., Some families of p-valent functions with negative coefficients, Acta Math. Univ. Comenianae 78, no. 1, 121-135, (2009).

Aouf, M. K., Bounded p-valent Robertson functions defined by using a differential operator, J. Franklin Institute 347, 1972-141, (2010). DOI: https://doi.org/10.1016/j.jfranklin.2010.10.012

Fukui, S., A remark on a class of certain analytic functions, Proc. Japan Acad. Ser. A , 66, 191-192, (1990). DOI: https://doi.org/10.3792/pjaa.66.191

Jack, I. S., Functions starlike and convex of order α,, J. London Math. Soc. 2, no. 3, 469-474, (1971). DOI: https://doi.org/10.1112/jlms/s2-3.3.469

Miller, S. S., Differential inequalities and Caratheodory functions, Bull. Amer. Math. Soc. 81, 79-81, (1975). DOI: https://doi.org/10.1090/S0002-9904-1975-13643-3

Miller, S. S. and Mocanu, P. T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65, 289-305, (1978). DOI: https://doi.org/10.1016/0022-247X(78)90181-6

Nunokawa, M., On the theory of multivalent functions, Tsukuba J. Math. 11, no. 2, 273-286, (1987). DOI: https://doi.org/10.21099/tkbjm/1496160581

Nunokawa, M. and Hoshino, S., On criterion on a class of certain analytic functions, RIMS Kyoto Univ. Kokyuroku, 881, 20-22, (1994).

Nishimoto, K. and Owa, S., A remark on p-valently α−convex functions, J. College Engrg. Nihon Univ. Ser. B 30, 107-110, (1989).

Owa, S., On certain classes of p-valent functions with negative coefficients, Simon Stevin, 59, no. 4, 385-402, (1985).

Owa, S., Some properties of certain multivalently functions, Appl. Math. Lett., 4, no.5, 79-83, (1991). DOI: https://doi.org/10.1016/0893-9659(91)90151-K

Saitoh, H., Nunokawa, M., Owa, S., Sekine, T. and Fukui, S., A remark on multivalent functions, Bull. Soc. Royale. Sci. Liege 56, no.2, 137-141, (1987).

Published
2021-12-16
Section
Articles