On multivalent starlike functions

Authors

  • Mamoru NUNOKAWA University of Gunma, Hoshikuki-cho 798-8 Chuou-Ward, Chiba, 260-0808, Japan, e-mail: mamoru-nuno@doctor.nifty.jp
  • Janusz SOKÓŁ University of Rzeszo´w Faculty of Mathematics and Natural Sciences ul. Prof. Pigonia 1, 35-310 Rzeszo´w, Poland, e-mail: jsokol@prz.edu.pl https://orcid.org/0000-0003-1204-2286

DOI:

https://doi.org/10.24193/subbmath.2019.1.09

Keywords:

Analytic functions, univalent functions, Ozaki’s condition.

Abstract

We prove some new sufficient conditions for function to be p-valent, or p-valently starlike in the unit disc.

Mathematics Subject Classification (2010): 30C45, 30C80.

References

Duren, P.L., Univalent Functions, Springer-Verlag, 1983.

Jack, I.S., Functions starlike and convex of order α, J. Lond. Math. Soc., 3(1971), 469- 474.

Marx, A., Untersuchungen u¨ber schlichte Abbildungen, Math. Ann., 107(1932/33), 40-65. [4] Miller, S.S., Mocanu, P.T., Differential Subordinations: Theory and Applications, Series of Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York/Basel, 2000.

Nunokawa, M., Srivastava, H.M., Tuneski, N., Jolevska-Tuneska, B., Some Marx- Strohhacker type results for a class of multivalent functions, Miskolc Math. Notes, 18(2017), no. 1, 353-364.

Nunokawa, M., On the theory of multivalent functions, Tsukuba J. Math., 11(1987), no. 2, 273-286.

Nunokawa, M., Sokol J., Cho, N.E., Some applications of Jack’s lemma, preprint.

Owa, S., Srivastava, H.M., Current Topics in Analytic Function Theory, World Sci. Publ., River Edge, NJ, 1992.

Srivastava, H.M., Patel, J., Mohapatra, G.P., A certain class of p-valently analytic functions, Math. Comput. Model., 41(2005), no. 2-3, 321-334.

Strohhacker, E., Beitrage zu¨r Theorie der schlichten Funktionen, Math. Z., 37(1933), 356-380.

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Published

2019-03-20

How to Cite

NUNOKAWA, M., & SOKÓŁ, J. (2019). On multivalent starlike functions. Studia Universitatis Babeș-Bolyai Mathematica, 64(1), 91–102. https://doi.org/10.24193/subbmath.2019.1.09

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