A new general idea for starlike and convex functions


  • Shigeyoshi Owa
  • Srivastava Hari Mohan
  • Toshio Hayami
  • Kazuo Kuroki




Analytic functions, Univalent functions, Starlike function of order $\alpha$, Convex function of order $\alpha$, Coefficient inequalities, General class of analytic functions.


Let $\mathcal{A}$ be the class of functions $f(z)$ which are analytic in the open unit disk $\mathbb{U}$ with $f(0)=0$ and $f'(0)=1$. For the class $\mathcal{A}$, a new general class $\mathcal{A}_{k}$ is defined. With this general class $\mathcal{A}_{k}$, two interesting classes $\mathcal{S}_{k}^{\ast}(\alpha)$ and $\mathcal{K}_{k}(\alpha)$ concerning classes of starlike of order $\alpha$ in $\mathbb{U}$ and convex of order $\alpha$ in $\mathbb{U}$ are considered.

Author Biographies

Shigeyoshi Owa

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

Srivastava Hari Mohan

Department ofMathematics and Statistics, University of Victoria, Victoria, British Columbia V8W3R4, Canada. ChinaMedical University, Taichung 40402, Taiwan, Republic of China.

Toshio Hayami

Department ofMathematics and Physics, Setsunan University, Neyagawa, Osaka 572-8508, Japan.

Kazuo Kuroki

Study Supporting Room, Osaka University of Health and Sport Sciences, Kumatori, Sennan, Osaka 590-0496, Japan.


P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.

A. W. Goodman, Univalent Functions, Vol. I and Vol. II, Mariner Publishing Company, Tampa, Florida, 1983.

S. S. Miller and P. T. Mocanu, Differential Subordination$:$Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, No. 225, Marcel Dekker Incorporated, New York and Basel, 2000.

S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39(1987), 1057--1077.

Ch. Pommerenke, Univalent Functions, Vanderhoeck and Ruprecht, Gottingen, 1975.

M. S. Robertson, On the theory of univalent functions, Ann. of Math. $($Ser. $1)$, 37(1936), 374--408.

St. Ruscheweyh, Convolutions in Geometric Function Theory, Seminaire de Mathematiques Superieures, Vol. 83, Presses de l'Universite de Montreal, Montreal, 1982

H. M. Srivastava and S. Owa (Editors), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1992.




How to Cite

Owa, S., Mohan, S. H., Hayami, T., & Kuroki, K. (2016). A new general idea for starlike and convex functions. Tamkang Journal of Mathematics, 47(4), 445-454. https://doi.org/10.5556/j.tkjm.47.2016.2157