Title: Argument Estimates for Carathéodory Functions with Applications
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-20-00055; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 211-215
Document Type: Research Paper
aDepartment of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea
bDepartment of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea
Received: 26 December 2020, Accepted: 20 February 2021, Published: 25 April 2021.
Corresponding Author: Nak Eun Cho (Email address: email@example.com)
Full Text: PDF
The purpose of the present paper is to investigate argument properties of Carathéodory functions applying the result obtained by Nunokawa et al.. We also obtain some geometric properties of analytic functions as special cases.
Keywords: Carathéodory functions, Argument estimatesReferences:
- M. Darus and D. K. Thomas, -logarithmically convex functions, Indian J. Pure Appl. Math. 29, 1049-1059, 1998.
- S. S. Miller, Differential inequalities and Carathéodory functions, Bull. Amer. Math. Soc. 81, 79-81, 1975.
- M. Nunokawa, On properties of non- Carathéodory functions, Proc. Japan Acad. Ser. A Math. Sci. 68, 152-153, 1992.
- M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad. Ser. A Math. Sci. 69, 234-237, 1993.
- M. Nunokawa, S. Owa, H. Saitoh, N. E. Cho and N. Takahashi, Some properties od analytic functions at extremal points for arguments, preprint.
- M. Nunokawa and D. K. Thomas, On convex and starlike functions in a sector, J. Austal. Math. Soc. Ser. A 60, 363-368, 1996.
- N. Takahashi and M. Nunokawa, A certain connection between starlike and convex functions, Applied Math. Lett. 16, 653-655, 2003.
- J. Sokol and L. Trojnar-Spelina, On a sufficient condition for strongly starlikeness, J. Inequal. Appl. 2013, Article No: 383, 2013.