Some generalization properties of analytic functions concerned with Sakaguchi result

Authors

  • Janusz Sokol
  • Mamoru Nunokawa
  • Shigeyoshi Owa
  • Kazuo Kuroki

DOI:

https://doi.org/10.5556/j.tkjm.46.2015.1657

Keywords:

analytic functions, starlike functions, univalent functions

Abstract

A subclass $\mathcal{A}(n,k)$ of analytic functions $f(z)$ in the unit disc $\mathbb{U}$ is considered. By means of the result due to K. Sakaguchi (J. Math. Soc. Japan {\bf 11}(1959), 72 -- 75) for $f(z) \in \mathcal{A}(1,1)$, some generalization properties of $f(z) \in \mathcal{A}(n,k)$ with several applications are discussed.

Author Biographies

Janusz Sokol

Department of Mathematics, Rzeszów University of Technology, Al. Powsta´nców Warszawy 12, 35-959 Rzeszów, Poland.

Mamoru Nunokawa

Emeritus Professor, University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba, 260-0808, Japan.

Shigeyoshi Owa

Department of Mathematics, Faculty of Education, Yamato University, Katayama 2-5-1, Suita, Osaka 564-0082,Japan.

Kazuo Kuroki

Department ofMathematics, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan.

References

S. Fukui and K. Sakaguchi, An extension of a theorem of S. Ruscheweyh, Bull. Fac. Edu. Wakayama Univ. Nat. Sci., 29(1980), 1--3.

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

T. H. MacGregor, A subordination for convex functions of order $alpha$, J. London Math. Soc. 2(1975), 530--536.

M. Nunokawa, On properties of non-Caratheodory functions, Proc. Japan Acad., 68(1992), 152--153.

M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad., 69(1993), 234--237.

S. Ponnusmy and V. Karunakakaran, Differential subordination and conformal mappings, Complex variable, 11(1989), 79--86.

K. Sakaguchi, On certain univalent mapping, J. Math. Soc. Japan, 11(1959), 72--75.

J. Sokol, On functions with the derivative satisfying a geometric condition, Appl. Math. Comput., 204(2008),116--119.

J. Sokol, On neighborhoods of analytic functions having positive real part, Math. Nachr., 284(2011), 1547--1553.

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Published

2015-06-30

How to Cite

Sokol, J., Nunokawa, M., Owa, S., & Kuroki, K. (2015). Some generalization properties of analytic functions concerned with Sakaguchi result. Tamkang Journal of Mathematics, 46(2), 143-150. https://doi.org/10.5556/j.tkjm.46.2015.1657

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Section

Papers