Some remarks on multivalent functions of higher-order derivatives
DOI:
https://doi.org/10.5269/bspm.42646Abstract
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.
References
1. Aouf, M. K., A generalization of mulivalent functions with negative coefficients, J. Korean Math. soc. 25, no. 1, 53-66, (1988).
2. Aouf, M. K., Certain subclasses of p-valent functions defined by using a differential operator, Appl. Math. Comput. 206, 867-875, (2008).
3. Aouf, M. K., Some families of p-valent functions with negative coefficients, Acta Math. Univ. Comenianae 78, no. 1, 121-135, (2009).
4. Aouf, M. K., Bounded p-valent Robertson functions defined by using a differential operator, J. Franklin Institute 347, 1972-141, (2010).
5. Fukui, S., A remark on a class of certain analytic functions, Proc. Japan Acad. Ser. A , 66, 191-192, (1990).
6. Jack, I. S., Functions starlike and convex of order α,, J. London Math. Soc. 2, no. 3, 469-474, (1971).
7. Miller, S. S., Differential inequalities and Caratheodory functions, Bull. Amer. Math. Soc. 81, 79-81, (1975).
8. Miller, S. S. and Mocanu, P. T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65, 289-305, (1978).
9. Nunokawa, M., On the theory of multivalent functions, Tsukuba J. Math. 11, no. 2, 273-286, (1987).
10. Nunokawa, M. and Hoshino, S., On criterion on a class of certain analytic functions, RIMS Kyoto Univ. Kokyuroku, 881, 20-22, (1994).
11. Nishimoto, K. and Owa, S., A remark on p-valently α−convex functions, J. College Engrg. Nihon Univ. Ser. B 30, 107-110, (1989).
12. Owa, S., On certain classes of p-valent functions with negative coefficients, Simon Stevin, 59, no. 4, 385-402, (1985).
13. Owa, S., Some properties of certain multivalently functions, Appl. Math. Lett., 4, no.5, 79-83, (1991).
14. 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).
2. Aouf, M. K., Certain subclasses of p-valent functions defined by using a differential operator, Appl. Math. Comput. 206, 867-875, (2008).
3. Aouf, M. K., Some families of p-valent functions with negative coefficients, Acta Math. Univ. Comenianae 78, no. 1, 121-135, (2009).
4. Aouf, M. K., Bounded p-valent Robertson functions defined by using a differential operator, J. Franklin Institute 347, 1972-141, (2010).
5. Fukui, S., A remark on a class of certain analytic functions, Proc. Japan Acad. Ser. A , 66, 191-192, (1990).
6. Jack, I. S., Functions starlike and convex of order α,, J. London Math. Soc. 2, no. 3, 469-474, (1971).
7. Miller, S. S., Differential inequalities and Caratheodory functions, Bull. Amer. Math. Soc. 81, 79-81, (1975).
8. Miller, S. S. and Mocanu, P. T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65, 289-305, (1978).
9. Nunokawa, M., On the theory of multivalent functions, Tsukuba J. Math. 11, no. 2, 273-286, (1987).
10. Nunokawa, M. and Hoshino, S., On criterion on a class of certain analytic functions, RIMS Kyoto Univ. Kokyuroku, 881, 20-22, (1994).
11. Nishimoto, K. and Owa, S., A remark on p-valently α−convex functions, J. College Engrg. Nihon Univ. Ser. B 30, 107-110, (1989).
12. Owa, S., On certain classes of p-valent functions with negative coefficients, Simon Stevin, 59, no. 4, 385-402, (1985).
13. Owa, S., Some properties of certain multivalently functions, Appl. Math. Lett., 4, no.5, 79-83, (1991).
14. 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).
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2021-12-16
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