Some remarks on multivalent functions of higher-order derivatives
Resumen
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.
Descargas
Citas
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).
Derechos de autor 2021 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
